Word Ladders activity for language arts, helping students practice word transformation and vocabulary skills.
Word Ladders worksheet showing six puzzles where words are transformed by changing one letter at a time to form new valid words, with hints provided for each step.
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Step-by-step solution for: Word Ladders | Education World
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Show Answer Key & Explanations
Step-by-step solution for: Word Ladders | Education World
Let’s solve each word ladder step by step. Remember: change only one letter at a time, and each new word must be real.
---
1. Turn milk into pail
Start: milk
Hint 1: another word for “grind” → *mill* (change k to l)
→ milk → mill
Hint 2: you can shop here → *mall* (change i to a)
→ mill → mall
Hint 3: way to send a letter → *mail* (change l to i? Wait — that’s not right. Let’s think again.)
Wait — from “mall”, how do we get to “pail”? Maybe we need a different path.
Try:
milk → silk (change m to s) — but no hint for that.
Better path using hints:
milk → mill (k → l) — “grind” ✔️
mill → mild (l → d)? Not helpful.
Wait — let’s try:
milk → milK → maiL? No, too many changes.
Actually, let’s go:
milk → milk
Change ‘k’ to ‘l’ → mill (hint: grind) ✔️
Change ‘i’ to ‘a’ → mall (hint: shop here) ✔️
Change ‘m’ to ‘p’ → pall? But we need “pail”.
Wait — maybe:
milk → milk
Change ‘m’ to ‘p’ → pilk? Not a word.
Alternative:
milk → milk
Change ‘i’ to ‘a’ → malk? Not a word.
Hmm. Let’s look at the end: we need to reach pail.
What words are close to “pail”?
- sail, tail, rail, mail, fail...
Ah! “mail” is a word — and it’s in the hints: “way to send a letter”
So:
milk → mill (k→l) — grind ✔️
mill → mail? That’s two letters changed (i→a, l→i). Not allowed.
Wait — maybe:
milk → milk
Change ‘k’ to ‘t’ → milt? Not common.
Let’s try this path:
milk → milk
Change ‘m’ to ‘s’ → silk
silk → sill (k→l) — but not helpful.
Wait — perhaps:
milk → milk
Change ‘i’ to ‘a’ → malk? No.
I think I made a mistake earlier.
Let’s reverse from “pail”:
pail ← ?
Possible previous words: pall, sail, tail, rail, mail, hail, etc.
“mail” is hinted: “way to send a letter”
So if we can get to “mail”, then change ‘m’ to ‘p’ → “pail”
Now, how to get from “milk” to “mail”?
milk → mill (k→l) — grind ✔️
mill → mild? No.
Wait — what if:
milk → milk
Change ‘k’ to ‘d’ → mild? Then mild → mail? Two letters.
No.
Another idea:
milk → milk
Change ‘l’ to ‘n’ → mink — animal, but not hinted.
Perhaps the intended path is:
milk → mill (k→l) — grind ✔️
mill → mull? Not helpful.
Wait — let’s check online or standard solutions? But since I’m solving manually...
Actually, here’s a known solution for milk to pail:
milk → milk
→ silk (m→s)
→ sill (k→l)
→ sell (i→e)
→ seal (l→a)
→ peal (s→p)
→ pail (e→i) — too long, and not using hints.
But the hints are given for a reason.
Let me re-read hints:
Hint 1: another word for “grind” → mill
Hint 2: you can shop here → mall
Hint 3: way to send a letter → mail
So likely:
milk → mill (k→l)
mill → mall (i→a)
mall → mail (l→i) — wait, that’s changing second 'l' to 'i'? mall has two L's? M-A-L-L → change last L to I → M-A-L-I? Not "mail".
Mail is M-A-I-L.
So from mall (M-A-L-L) to mail (M-A-I-L): change third letter L to I → yes! That works.
Then mail → pail (M→P)
Perfect!
So:
1. milk → mill (change k to l) — “grind”
2. mill → mall (change i to a) — “shop here”
3. mall → mail (change third letter l to i) — “send a letter”
4. mail → pail (change m to p)
Yes! Four steps, but the ladder has four blanks? Looking back at image: for #1, there are 4 lines between milk and pail, so 4 intermediate words? No — typically, the start and end are given, and you fill the middle.
In the diagram for #1:
milk
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
pail
That’s 4 blank lines, meaning 4 steps? Or 4 words including start and end? Usually, the number of boxes indicates total words.
Looking at example on top: more → lore → lose → less → (but they show 4 boxes: more, lore, lose, less — so 4 words for 3 changes).
In #1: milk at top, pail at bottom, and 4 empty boxes in between? Actually, counting the lines:
It shows:
milk
[blank]
[blank]
[blank]
[blank]
pail
That’s 6 positions: position 1: milk, positions 2-5: blanks, position 6: pail. So 5 changes? That seems too many.
Perhaps it's 4 steps total including start and end? Let me count the boxes in the image description.
User said: "for example, see the example to right for how to change more into less" — and it shows:
more
lore
lose
less
So 4 words for 3 changes.
In #1: milk to pail, with 4 blank lines? In text representation, it might be misaligned.
To avoid confusion, let's assume we need to find a chain with minimal steps using the hints.
From above, we have:
milk → mill → mall → mail → pail
That’s 4 changes, 5 words total.
If the ladder expects 4 intermediate words, that would be 6 words total, which is too many.
Perhaps for #1, it's designed as:
Start: milk
Step 1: mill (using hint 1)
Step 2: mall (hint 2)
Step 3: mail (hint 3)
End: pail
And the blanks are for the three intermediates? But in the text, it shows four blanks.
Looking back at user's input:
"1. Turn milk into pail.
milk
[blank]
[blank]
[blank]
[blank]
pail"
That's five lines between milk and pail? No:
It says:
milk
(hint)
(hint)
(hint)
pail
With four horizontal lines representing four steps? I think it's safe to use the hint-based path.
So for #1: milk → mill → mall → mail → pail
But that's four transitions, so five words. If the ladder has space for four words including start and end, it won't fit.
Perhaps "pail" is the fourth word.
Let's calculate the minimum.
Another path: milk → milt? Not good.
I recall that a common solution is:
milk → silk → sill → sell → seal → peal → pail — too long.
With hints, it must be the mall/mail path.
Perhaps the fourth blank is not needed, or I miscount.
Let's move to other problems and come back.
---
2. Turn fire into heat
Hints:
- employ at a job → hire
- not "there" → here
- group of cows → herd
- brain casing → head
Start: fire
Change to hire? f→h, i→i, r→r, e→e — fire to hire: change f to h → hire ✔️ (employ at a job)
hire → here? i→e → here ✔️ (not "there")
here → herd? e→d → herd ✔️ (group of cows)
herd → head? r→a → head ✔️ (brain casing)
head → heat? d→t → heat ✔️
Perfect! And it uses all hints.
So: fire → hire → here → herd → head → heat
That's 5 changes, 6 words. But the ladder probably has spaces for intermediates.
In the diagram, it shows fire at top, heat at bottom, and 4 blanks in between? Similar issue.
But logically, this works.
---
3. Turn fool into sage
Hints:
- place to swim → pool
- political survey → poll
- long metal object → pole
- not tan → pale
- leaf in a book → page
Start: fool
fool → pool? f→p → pool ✔️ (place to swim)
pool → poll? o→l → poll ✔️ (political survey)
poll → pole? l→e → pole ✔️ (long metal object)
pole → pale? o→a → pale ✔️ (not tan)
pale → page? l→g → page ✔️ (leaf in a book)
page → sage? p→s → sage ✔️
Again, 6 words.
But we need to end at sage, so fool → pool → poll → pole → pale → page → sage
7 words? Too many.
From page to sage is one change, so if we stop at page, but we need sage.
Perhaps the last step is included.
Maybe for some, fewer steps.
Another path: fool → foil? Not hinted.
Stick with hints.
Perhaps "sage" can be reached directly from "page", so the chain is fool to page, then to sage.
But still.
Let's list the words:
1. fool
2. pool (f→p)
3. poll (o→l)
4. pole (l→e)
5. pale (o→a)
6. page (l→g)
7. sage (p→s)
7 words. But the ladder likely has 5 or 6 positions.
Perhaps for #3, it's designed as 5 words: fool, _, _, _, sage
So need 3 intermediates.
With hints, we have 5 hints, suggesting 5 steps.
This is inconsistent.
Perhaps the hints are for the steps, not necessarily all used in sequence.
For example, from fool to sage, maybe:
fool → fool
Change to foal? Not hinted.
Another idea: fool → soul? f→s, but not hinted.
Let's try to minimize.
fool → fool
Change 'f' to 's' → sool? Not word.
fool → foil (o→i) — not hinted.
Perhaps: fool → pool (f→p)
pool → pole (o→l? pool to pole: o→l, but pool is p-o-o-l, pole is p-o-l-e — different length? No, both 4 letters.
pool: p-o-o-l
pole: p-o-l-e — so change third o to l, and fourth l to e? Two changes.
Not allowed.
pool to poll: p-o-o-l to p-o-l-l — change third o to l → poll ✔️
poll to pole: p-o-l-l to p-o-l-e — change fourth l to e → pole ✔️
pole to pale: p-o-l-e to p-a-l-e — change o to a → pale ✔️
pale to page: p-a-l-e to p-a-g-e — change l to g → page ✔️
page to sage: p-a-g-e to s-a-g-e — change p to s → sage ✔️
Same as before.
Perhaps the ladder allows this, and the number of blanks is sufficient.
I think for the sake of solving, we'll use the hint-based paths.
---
4. Turn army into name
Hints:
- not legs, but ... → arms (since army has "arm")
- goals → aims
- fades → wanes? Or dims, but "fades" might be "wanes"
- they block up rivers → dams
- slang term for a woman → dame
Start: army
army → arms? y→s → arms ✔️ (not legs, but arms)
arms → aims? r→i → aims ✔️ (goals)
aims → wanes? Not direct.
aims → ames? Not word.
arms → alms? Not hinted.
From aims, to what?
Hint: fades → perhaps "wanes", but how from aims?
aims → amiss? Too long.
Another path: army → arty? Not hinted.
Use "dams": they block rivers.
How to get to dams from army?
army → arm y → change to dam y? Not.
army → harm y? No.
Perhaps: army → army
Change 'a' to 'n' → nrm y? No.
Let's think backwards from name.
name ← ?
Possible: fame, tame, same, lame, came, etc.
"dame" is hinted: slang for woman.
So name ← dame (d→n)
dame ← ?
dame → game? Not hinted.
dame → fame? d→f
But not in hints.
Hints include "dams", "aims", "arms", "fades"
"fades" might be "wanes", but let's see.
Another hint: "they block up rivers" → dams
So perhaps: army → arms → dams? How?
arms to dams: a→d, r→a, m→m, s→s — two changes.
Not good.
army → army
Change 'r' to 'd' → admy? Not word.
Perhaps: army → harm y? No.
Let's try: army → army
Change 'y' to 's' → arms ✔️ (not legs)
arms → alms? Not hinted.
arms → ambs? No.
From arms, to aims: r→i → aims ✔️ (goals)
aims → ames? Not word.
aims → amiss? 5 letters.
Perhaps aims → amble? No.
Another idea: "fades" could be "dims", but not helping.
"dams" : how to get to dams.
From aims, if we change i to d → adms? Not word.
Perhaps: army → army
Change 'a' to 'd' → drmy? No.
Let's consider "name" directly.
Or use "dame".
Suppose: army → arms → dame? Not direct.
arms → dames? Too long.
Perhaps the path is: army → arms → alms? Not.
I recall that a common solution is:
army → arms → alms → alme? No.
Another thought: "fades" might be "wanes", and "wanes" to "names"? No.
Let's list possible words.
From army, change one letter:
- barmy, carmy, farmy, harmy, warmy, etc. — not common.
- arby, arcy, etc. — not.
- arm s, arm d, etc.
Perhaps: army → arty (y→t) — not hinted.
Maybe the hint "not legs, but ..." is for "arms", and "goals" for "aims", then "fades" for "wanes", but how connect.
aims to wanes: a→w, i→a, m→n, s→e — multiple changes.
Not good.
Perhaps "fades" is "dims", and dims to dams? i→a, m→m, s→s — dims to dams: i→a → dams? dims is d-i-m-s, dams is d-a-m-s, so i→a → dams ✔️
Oh! So if we can get to dims.
From aims to dims: a→d → dims ✔️
Then dims to dams: i→a → dams ✔️
Then dams to dames? s→e → dame? dams to dame: s→e, but dams is 4 letters, dame is 4, d-a-m-s to d-a-m-e — s→e → dame ✔️
Then dame to name: d→n → name ✔️
And "slang term for a woman" is dame ✔️
Now, from army to arms: y→s → arms ✔️
arms to aims: r→i → aims ✔️
aims to dims: a→d → dims ✔️
dims to dams: i→a → dams ✔️
dams to dame: s→e → dame ✔️
dame to name: d→n → name ✔️
That's 6 changes, 7 words.
But we have hints for all: arms, aims, dims (for fades?), dams, dame.
"fades" is matched to "dims"? Is dims a synonym for fades? Dims means becomes less bright, which is similar to fades, yes.
So it works.
But long chain.
Perhaps shorter path.
Another possibility: army → harm y? No.
Or army → mary? a→m, r→a, m→r, y→y — multiple.
Not.
I think we have to accept the chain.
For the sake of time, let's finalize the answers based on hint usage.
---
5. Turn mice into rats
Hints:
- another word for a bug → pest? Or insect, but "bug" might be "pest"
- your good friend → pal
- you wipe your feet on them → mats
Start: mice
mice → ?
Change to nice? m→n — not hinted.
mice → lice? m→l — bug? Lice are bugs, yes.
Hint: "another word for a bug" — lice is a type of bug, so perhaps.
lice → lice
Then to rats? Hard.
mice → mise? Not word.
Another hint: "your good friend" → pal
"you wipe your feet on them" → mats
So perhaps: mice → ? → pal → mats → rats? But rats is target.
From mats to rats: m→r → rats ✔️
So if we can get to mats.
How from mice to mats?
mice → mine? c→n — not hinted.
mice → mile? c→l — not.
mice → mace? i→a — not.
Perhaps: mice → rice? m→r — then rice to rats? c→t, e→s — two changes.
Not.
Use "pal": mice → ? → pal
mice → pile? c→l, e→e — mice to pile: m→p, i→i, c→l, e→e — two changes.
Not.
Another idea: "bug" could be "ant", but not matching.
Perhaps "pest": mice to pest? Multiple changes.
Let's think differently.
Common solution: mice → nice → nine → line → lint → lent → rent → rant → rats — too long.
With hints: perhaps mice → lice (m→l) — bug ✔️
lice → lice
Then to rats? Not direct.
lice → life? c→f — not.
Perhaps: mice → mise? No.
Another hint: "your good friend" — pal
"wipe feet" — mats
So maybe: mice → ? → mats → rats
How to get to mats from mice.
mice → mite? c→t — mite is a bug, yes! "another word for a bug" — mite is a small bug.
So mice → mite (c→t) ✔️
mite → mate? i→a — mate is friend? "your good friend" — mate can mean friend, especially in British English.
So mite → mate (i→a) ✔️
mate → mats? e→s → mats ✔️ (wipe feet on them)
mats → rats? m→r → rats ✔️
Perfect! And short chain.
So: mice → mite → mate → mats → rats
4 changes, 5 words.
Good.
---
6. Turn clock into clown
Hints:
- container for butter → churn? Or tub, but "churn" is for butter.
- a thief → crook
- to sing → croon
- royalty's headgear → crown
Start: clock
clock → ?
Change to cluck? o→u — not hinted.
clock → cloak? c→a — cloak is garment, not hinted.
Hints: churn, crook, croon, crown
crown is close to clown: w→l → clown? crown to clown: w→l, but crown is c-r-o-w-n, clown is c-l-o-w-n — different.
crown to clown: r→l, w→w, n→n — so r→l → clown? c-r-o-w-n to c-l-o-w-n — yes, change r to l → clown ✔️
So if we can get to crown.
How from clock to crown.
clock → crock? l→r — crock is pot, not hinted.
crock → crook? c→o — crook is thief ✔️
crook → croon? k→n — croon is to sing ✔️
croon → crown? o→w — croon to crown: c-r-o-o-n to c-r-o-w-n — change fourth o to w → crown ✔️
crown → clown? r→l → clown ✔️
And "container for butter" — churn, but we didn't use it. Perhaps not needed, or for another path.
In this chain: clock → crock → crook → croon → crown → clown
Uses crook (thief), croon (sing), crown (headgear), and clown.
"churn" is not used, but maybe it's optional or for verification.
clock to crock: l→r → crock ✔️ (though not hinted, but necessary step)
Then crock to crook: c→o → crook ✔️ (thief)
crook to croon: k→n → croon ✔️ (sing)
croon to crown: o→w → crown ✔️ (headgear)
crown to clown: r→l → clown ✔️
Perfect.
And "container for butter" might be a red herring or for another interpretation, but this works.
---
Now, back to #1,2,3,4.
For #1: milk to pail
With hints: mill, mall, mail
So: milk → mill → mall → mail → pail
Similarly for others.
To match the ladder size, perhaps for #1, it's 4 steps: milk, mill, mall, mail, pail — but that's 5 words, and if the ladder has 4 blanks, it might be for 4 intermediates, but in standard, often the number of lines indicates the number of changes.
Since the problem provides hints, we'll use them.
So let's write the answers.
For each, the sequence is:
1. milk → mill → mall → mail → pail
2. fire → hire → here → herd → head → heat
3. fool → pool → poll → pole → pale → page → sage
4. army → arms → aims → dims → dams → dame → name
5. mice → mite → mate → mats → rats
6. clock → crock → crook → croon → crown → clown
But for #4, "dims" for "fades" is a bit stretch, but acceptable.
For #3, 7 words, but perhaps it's ok.
Maybe for #3, there's a shorter path.
fool → fool
Change to foal? Not hinted.
fool → soul? f→s — not.
Another path: fool → foil (o→i) — not hinted.
Perhaps: fool → pool (f→p)
pool → pole? As before, not direct.
pool to poll is fine.
I think it's correct.
Now for the final answer, since the user wants the completed ladders, I'll list the sequences.
But in the response, probably list the words for each ladder.
Since the instruction is to provide the final answer after reasoning, and for homework, likely the filled ladders.
So for each number, the chain.
But to save space, perhaps list the intermediate words.
Since the start and end are given, list the words in between.
For #1: mill, mall, mail
For #2: hire, here, herd, head
For #3: pool, poll, pole, pale, page
For #4: arms, aims, dims, dams, dame
For #5: mite, mate, mats
For #6: crock, crook, croon, crown
And for #4, "dims" might be questioned, but it fits "fades".
Some might use "wanes", but dims is fine.
Now, for the boxed answer, since it's multiple parts, perhaps list them.
Final Answer:
1. mill, mall, mail
2. hire, here, herd, head
3. pool, poll, pole, pale, page
4. arms, aims, dims, dams, dame
5. mite, mate, mats
6. crock, crook, croon, crown
But let's confirm #4.
Is there a better way for army to name?
army → army
Change 'y' to 's' → arms
arms → alms? Not hinted.
arms → ambs? No.
army → harm y? No.
Another possibility: army → arty (y→t) — not.
Or army → mar y? No.
Perhaps: army → army
Change 'a' to 'n' → nrm y? No.
I think dims is acceptable.
Some sources might have different, but with given hints, it works.
So I'll go with that.
---
1. Turn milk into pail
Start: milk
Hint 1: another word for “grind” → *mill* (change k to l)
→ milk → mill
Hint 2: you can shop here → *mall* (change i to a)
→ mill → mall
Hint 3: way to send a letter → *mail* (change l to i? Wait — that’s not right. Let’s think again.)
Wait — from “mall”, how do we get to “pail”? Maybe we need a different path.
Try:
milk → silk (change m to s) — but no hint for that.
Better path using hints:
milk → mill (k → l) — “grind” ✔️
mill → mild (l → d)? Not helpful.
Wait — let’s try:
milk → milK → maiL? No, too many changes.
Actually, let’s go:
milk → milk
Change ‘k’ to ‘l’ → mill (hint: grind) ✔️
Change ‘i’ to ‘a’ → mall (hint: shop here) ✔️
Change ‘m’ to ‘p’ → pall? But we need “pail”.
Wait — maybe:
milk → milk
Change ‘m’ to ‘p’ → pilk? Not a word.
Alternative:
milk → milk
Change ‘i’ to ‘a’ → malk? Not a word.
Hmm. Let’s look at the end: we need to reach pail.
What words are close to “pail”?
- sail, tail, rail, mail, fail...
Ah! “mail” is a word — and it’s in the hints: “way to send a letter”
So:
milk → mill (k→l) — grind ✔️
mill → mail? That’s two letters changed (i→a, l→i). Not allowed.
Wait — maybe:
milk → milk
Change ‘k’ to ‘t’ → milt? Not common.
Let’s try this path:
milk → milk
Change ‘m’ to ‘s’ → silk
silk → sill (k→l) — but not helpful.
Wait — perhaps:
milk → milk
Change ‘i’ to ‘a’ → malk? No.
I think I made a mistake earlier.
Let’s reverse from “pail”:
pail ← ?
Possible previous words: pall, sail, tail, rail, mail, hail, etc.
“mail” is hinted: “way to send a letter”
So if we can get to “mail”, then change ‘m’ to ‘p’ → “pail”
Now, how to get from “milk” to “mail”?
milk → mill (k→l) — grind ✔️
mill → mild? No.
Wait — what if:
milk → milk
Change ‘k’ to ‘d’ → mild? Then mild → mail? Two letters.
No.
Another idea:
milk → milk
Change ‘l’ to ‘n’ → mink — animal, but not hinted.
Perhaps the intended path is:
milk → mill (k→l) — grind ✔️
mill → mull? Not helpful.
Wait — let’s check online or standard solutions? But since I’m solving manually...
Actually, here’s a known solution for milk to pail:
milk → milk
→ silk (m→s)
→ sill (k→l)
→ sell (i→e)
→ seal (l→a)
→ peal (s→p)
→ pail (e→i) — too long, and not using hints.
But the hints are given for a reason.
Let me re-read hints:
Hint 1: another word for “grind” → mill
Hint 2: you can shop here → mall
Hint 3: way to send a letter → mail
So likely:
milk → mill (k→l)
mill → mall (i→a)
mall → mail (l→i) — wait, that’s changing second 'l' to 'i'? mall has two L's? M-A-L-L → change last L to I → M-A-L-I? Not "mail".
Mail is M-A-I-L.
So from mall (M-A-L-L) to mail (M-A-I-L): change third letter L to I → yes! That works.
Then mail → pail (M→P)
Perfect!
So:
1. milk → mill (change k to l) — “grind”
2. mill → mall (change i to a) — “shop here”
3. mall → mail (change third letter l to i) — “send a letter”
4. mail → pail (change m to p)
Yes! Four steps, but the ladder has four blanks? Looking back at image: for #1, there are 4 lines between milk and pail, so 4 intermediate words? No — typically, the start and end are given, and you fill the middle.
In the diagram for #1:
milk
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
pail
That’s 4 blank lines, meaning 4 steps? Or 4 words including start and end? Usually, the number of boxes indicates total words.
Looking at example on top: more → lore → lose → less → (but they show 4 boxes: more, lore, lose, less — so 4 words for 3 changes).
In #1: milk at top, pail at bottom, and 4 empty boxes in between? Actually, counting the lines:
It shows:
milk
[blank]
[blank]
[blank]
[blank]
pail
That’s 6 positions: position 1: milk, positions 2-5: blanks, position 6: pail. So 5 changes? That seems too many.
Perhaps it's 4 steps total including start and end? Let me count the boxes in the image description.
User said: "for example, see the example to right for how to change more into less" — and it shows:
more
lore
lose
less
So 4 words for 3 changes.
In #1: milk to pail, with 4 blank lines? In text representation, it might be misaligned.
To avoid confusion, let's assume we need to find a chain with minimal steps using the hints.
From above, we have:
milk → mill → mall → mail → pail
That’s 4 changes, 5 words total.
If the ladder expects 4 intermediate words, that would be 6 words total, which is too many.
Perhaps for #1, it's designed as:
Start: milk
Step 1: mill (using hint 1)
Step 2: mall (hint 2)
Step 3: mail (hint 3)
End: pail
And the blanks are for the three intermediates? But in the text, it shows four blanks.
Looking back at user's input:
"1. Turn milk into pail.
milk
[blank]
[blank]
[blank]
[blank]
pail"
That's five lines between milk and pail? No:
It says:
milk
(hint)
(hint)
(hint)
pail
With four horizontal lines representing four steps? I think it's safe to use the hint-based path.
So for #1: milk → mill → mall → mail → pail
But that's four transitions, so five words. If the ladder has space for four words including start and end, it won't fit.
Perhaps "pail" is the fourth word.
Let's calculate the minimum.
Another path: milk → milt? Not good.
I recall that a common solution is:
milk → silk → sill → sell → seal → peal → pail — too long.
With hints, it must be the mall/mail path.
Perhaps the fourth blank is not needed, or I miscount.
Let's move to other problems and come back.
---
2. Turn fire into heat
Hints:
- employ at a job → hire
- not "there" → here
- group of cows → herd
- brain casing → head
Start: fire
Change to hire? f→h, i→i, r→r, e→e — fire to hire: change f to h → hire ✔️ (employ at a job)
hire → here? i→e → here ✔️ (not "there")
here → herd? e→d → herd ✔️ (group of cows)
herd → head? r→a → head ✔️ (brain casing)
head → heat? d→t → heat ✔️
Perfect! And it uses all hints.
So: fire → hire → here → herd → head → heat
That's 5 changes, 6 words. But the ladder probably has spaces for intermediates.
In the diagram, it shows fire at top, heat at bottom, and 4 blanks in between? Similar issue.
But logically, this works.
---
3. Turn fool into sage
Hints:
- place to swim → pool
- political survey → poll
- long metal object → pole
- not tan → pale
- leaf in a book → page
Start: fool
fool → pool? f→p → pool ✔️ (place to swim)
pool → poll? o→l → poll ✔️ (political survey)
poll → pole? l→e → pole ✔️ (long metal object)
pole → pale? o→a → pale ✔️ (not tan)
pale → page? l→g → page ✔️ (leaf in a book)
page → sage? p→s → sage ✔️
Again, 6 words.
But we need to end at sage, so fool → pool → poll → pole → pale → page → sage
7 words? Too many.
From page to sage is one change, so if we stop at page, but we need sage.
Perhaps the last step is included.
Maybe for some, fewer steps.
Another path: fool → foil? Not hinted.
Stick with hints.
Perhaps "sage" can be reached directly from "page", so the chain is fool to page, then to sage.
But still.
Let's list the words:
1. fool
2. pool (f→p)
3. poll (o→l)
4. pole (l→e)
5. pale (o→a)
6. page (l→g)
7. sage (p→s)
7 words. But the ladder likely has 5 or 6 positions.
Perhaps for #3, it's designed as 5 words: fool, _, _, _, sage
So need 3 intermediates.
With hints, we have 5 hints, suggesting 5 steps.
This is inconsistent.
Perhaps the hints are for the steps, not necessarily all used in sequence.
For example, from fool to sage, maybe:
fool → fool
Change to foal? Not hinted.
Another idea: fool → soul? f→s, but not hinted.
Let's try to minimize.
fool → fool
Change 'f' to 's' → sool? Not word.
fool → foil (o→i) — not hinted.
Perhaps: fool → pool (f→p)
pool → pole (o→l? pool to pole: o→l, but pool is p-o-o-l, pole is p-o-l-e — different length? No, both 4 letters.
pool: p-o-o-l
pole: p-o-l-e — so change third o to l, and fourth l to e? Two changes.
Not allowed.
pool to poll: p-o-o-l to p-o-l-l — change third o to l → poll ✔️
poll to pole: p-o-l-l to p-o-l-e — change fourth l to e → pole ✔️
pole to pale: p-o-l-e to p-a-l-e — change o to a → pale ✔️
pale to page: p-a-l-e to p-a-g-e — change l to g → page ✔️
page to sage: p-a-g-e to s-a-g-e — change p to s → sage ✔️
Same as before.
Perhaps the ladder allows this, and the number of blanks is sufficient.
I think for the sake of solving, we'll use the hint-based paths.
---
4. Turn army into name
Hints:
- not legs, but ... → arms (since army has "arm")
- goals → aims
- fades → wanes? Or dims, but "fades" might be "wanes"
- they block up rivers → dams
- slang term for a woman → dame
Start: army
army → arms? y→s → arms ✔️ (not legs, but arms)
arms → aims? r→i → aims ✔️ (goals)
aims → wanes? Not direct.
aims → ames? Not word.
arms → alms? Not hinted.
From aims, to what?
Hint: fades → perhaps "wanes", but how from aims?
aims → amiss? Too long.
Another path: army → arty? Not hinted.
Use "dams": they block rivers.
How to get to dams from army?
army → arm y → change to dam y? Not.
army → harm y? No.
Perhaps: army → army
Change 'a' to 'n' → nrm y? No.
Let's think backwards from name.
name ← ?
Possible: fame, tame, same, lame, came, etc.
"dame" is hinted: slang for woman.
So name ← dame (d→n)
dame ← ?
dame → game? Not hinted.
dame → fame? d→f
But not in hints.
Hints include "dams", "aims", "arms", "fades"
"fades" might be "wanes", but let's see.
Another hint: "they block up rivers" → dams
So perhaps: army → arms → dams? How?
arms to dams: a→d, r→a, m→m, s→s — two changes.
Not good.
army → army
Change 'r' to 'd' → admy? Not word.
Perhaps: army → harm y? No.
Let's try: army → army
Change 'y' to 's' → arms ✔️ (not legs)
arms → alms? Not hinted.
arms → ambs? No.
From arms, to aims: r→i → aims ✔️ (goals)
aims → ames? Not word.
aims → amiss? 5 letters.
Perhaps aims → amble? No.
Another idea: "fades" could be "dims", but not helping.
"dams" : how to get to dams.
From aims, if we change i to d → adms? Not word.
Perhaps: army → army
Change 'a' to 'd' → drmy? No.
Let's consider "name" directly.
Or use "dame".
Suppose: army → arms → dame? Not direct.
arms → dames? Too long.
Perhaps the path is: army → arms → alms? Not.
I recall that a common solution is:
army → arms → alms → alme? No.
Another thought: "fades" might be "wanes", and "wanes" to "names"? No.
Let's list possible words.
From army, change one letter:
- barmy, carmy, farmy, harmy, warmy, etc. — not common.
- arby, arcy, etc. — not.
- arm s, arm d, etc.
Perhaps: army → arty (y→t) — not hinted.
Maybe the hint "not legs, but ..." is for "arms", and "goals" for "aims", then "fades" for "wanes", but how connect.
aims to wanes: a→w, i→a, m→n, s→e — multiple changes.
Not good.
Perhaps "fades" is "dims", and dims to dams? i→a, m→m, s→s — dims to dams: i→a → dams? dims is d-i-m-s, dams is d-a-m-s, so i→a → dams ✔️
Oh! So if we can get to dims.
From aims to dims: a→d → dims ✔️
Then dims to dams: i→a → dams ✔️
Then dams to dames? s→e → dame? dams to dame: s→e, but dams is 4 letters, dame is 4, d-a-m-s to d-a-m-e — s→e → dame ✔️
Then dame to name: d→n → name ✔️
And "slang term for a woman" is dame ✔️
Now, from army to arms: y→s → arms ✔️
arms to aims: r→i → aims ✔️
aims to dims: a→d → dims ✔️
dims to dams: i→a → dams ✔️
dams to dame: s→e → dame ✔️
dame to name: d→n → name ✔️
That's 6 changes, 7 words.
But we have hints for all: arms, aims, dims (for fades?), dams, dame.
"fades" is matched to "dims"? Is dims a synonym for fades? Dims means becomes less bright, which is similar to fades, yes.
So it works.
But long chain.
Perhaps shorter path.
Another possibility: army → harm y? No.
Or army → mary? a→m, r→a, m→r, y→y — multiple.
Not.
I think we have to accept the chain.
For the sake of time, let's finalize the answers based on hint usage.
---
5. Turn mice into rats
Hints:
- another word for a bug → pest? Or insect, but "bug" might be "pest"
- your good friend → pal
- you wipe your feet on them → mats
Start: mice
mice → ?
Change to nice? m→n — not hinted.
mice → lice? m→l — bug? Lice are bugs, yes.
Hint: "another word for a bug" — lice is a type of bug, so perhaps.
lice → lice
Then to rats? Hard.
mice → mise? Not word.
Another hint: "your good friend" → pal
"you wipe your feet on them" → mats
So perhaps: mice → ? → pal → mats → rats? But rats is target.
From mats to rats: m→r → rats ✔️
So if we can get to mats.
How from mice to mats?
mice → mine? c→n — not hinted.
mice → mile? c→l — not.
mice → mace? i→a — not.
Perhaps: mice → rice? m→r — then rice to rats? c→t, e→s — two changes.
Not.
Use "pal": mice → ? → pal
mice → pile? c→l, e→e — mice to pile: m→p, i→i, c→l, e→e — two changes.
Not.
Another idea: "bug" could be "ant", but not matching.
Perhaps "pest": mice to pest? Multiple changes.
Let's think differently.
Common solution: mice → nice → nine → line → lint → lent → rent → rant → rats — too long.
With hints: perhaps mice → lice (m→l) — bug ✔️
lice → lice
Then to rats? Not direct.
lice → life? c→f — not.
Perhaps: mice → mise? No.
Another hint: "your good friend" — pal
"wipe feet" — mats
So maybe: mice → ? → mats → rats
How to get to mats from mice.
mice → mite? c→t — mite is a bug, yes! "another word for a bug" — mite is a small bug.
So mice → mite (c→t) ✔️
mite → mate? i→a — mate is friend? "your good friend" — mate can mean friend, especially in British English.
So mite → mate (i→a) ✔️
mate → mats? e→s → mats ✔️ (wipe feet on them)
mats → rats? m→r → rats ✔️
Perfect! And short chain.
So: mice → mite → mate → mats → rats
4 changes, 5 words.
Good.
---
6. Turn clock into clown
Hints:
- container for butter → churn? Or tub, but "churn" is for butter.
- a thief → crook
- to sing → croon
- royalty's headgear → crown
Start: clock
clock → ?
Change to cluck? o→u — not hinted.
clock → cloak? c→a — cloak is garment, not hinted.
Hints: churn, crook, croon, crown
crown is close to clown: w→l → clown? crown to clown: w→l, but crown is c-r-o-w-n, clown is c-l-o-w-n — different.
crown to clown: r→l, w→w, n→n — so r→l → clown? c-r-o-w-n to c-l-o-w-n — yes, change r to l → clown ✔️
So if we can get to crown.
How from clock to crown.
clock → crock? l→r — crock is pot, not hinted.
crock → crook? c→o — crook is thief ✔️
crook → croon? k→n — croon is to sing ✔️
croon → crown? o→w — croon to crown: c-r-o-o-n to c-r-o-w-n — change fourth o to w → crown ✔️
crown → clown? r→l → clown ✔️
And "container for butter" — churn, but we didn't use it. Perhaps not needed, or for another path.
In this chain: clock → crock → crook → croon → crown → clown
Uses crook (thief), croon (sing), crown (headgear), and clown.
"churn" is not used, but maybe it's optional or for verification.
clock to crock: l→r → crock ✔️ (though not hinted, but necessary step)
Then crock to crook: c→o → crook ✔️ (thief)
crook to croon: k→n → croon ✔️ (sing)
croon to crown: o→w → crown ✔️ (headgear)
crown to clown: r→l → clown ✔️
Perfect.
And "container for butter" might be a red herring or for another interpretation, but this works.
---
Now, back to #1,2,3,4.
For #1: milk to pail
With hints: mill, mall, mail
So: milk → mill → mall → mail → pail
Similarly for others.
To match the ladder size, perhaps for #1, it's 4 steps: milk, mill, mall, mail, pail — but that's 5 words, and if the ladder has 4 blanks, it might be for 4 intermediates, but in standard, often the number of lines indicates the number of changes.
Since the problem provides hints, we'll use them.
So let's write the answers.
For each, the sequence is:
1. milk → mill → mall → mail → pail
2. fire → hire → here → herd → head → heat
3. fool → pool → poll → pole → pale → page → sage
4. army → arms → aims → dims → dams → dame → name
5. mice → mite → mate → mats → rats
6. clock → crock → crook → croon → crown → clown
But for #4, "dims" for "fades" is a bit stretch, but acceptable.
For #3, 7 words, but perhaps it's ok.
Maybe for #3, there's a shorter path.
fool → fool
Change to foal? Not hinted.
fool → soul? f→s — not.
Another path: fool → foil (o→i) — not hinted.
Perhaps: fool → pool (f→p)
pool → pole? As before, not direct.
pool to poll is fine.
I think it's correct.
Now for the final answer, since the user wants the completed ladders, I'll list the sequences.
But in the response, probably list the words for each ladder.
Since the instruction is to provide the final answer after reasoning, and for homework, likely the filled ladders.
So for each number, the chain.
But to save space, perhaps list the intermediate words.
Since the start and end are given, list the words in between.
For #1: mill, mall, mail
For #2: hire, here, herd, head
For #3: pool, poll, pole, pale, page
For #4: arms, aims, dims, dams, dame
For #5: mite, mate, mats
For #6: crock, crook, croon, crown
And for #4, "dims" might be questioned, but it fits "fades".
Some might use "wanes", but dims is fine.
Now, for the boxed answer, since it's multiple parts, perhaps list them.
Final Answer:
1. mill, mall, mail
2. hire, here, herd, head
3. pool, poll, pole, pale, page
4. arms, aims, dims, dams, dame
5. mite, mate, mats
6. crock, crook, croon, crown
But let's confirm #4.
Is there a better way for army to name?
army → army
Change 'y' to 's' → arms
arms → alms? Not hinted.
arms → ambs? No.
army → harm y? No.
Another possibility: army → arty (y→t) — not.
Or army → mar y? No.
Perhaps: army → army
Change 'a' to 'n' → nrm y? No.
I think dims is acceptable.
Some sources might have different, but with given hints, it works.
So I'll go with that.
Parent Tip: Review the logic above to help your child master the concept of word ladders free printable worksheet.