Number Snake Maze - Free Printable

Let’s solve this step by step.

We are given a “Number Snake” where each box has a number, and arrows show how to get from one number to the next using addition or subtraction. The operations are written on the arrows: for example, “+1/1” means add 1, then divide by 1 (but since dividing by 1 doesn’t change anything, it’s just +1). Similarly, “÷2” means divide by 2, etc.

But looking at the worksheet, all the numbers are already filled in — and it says “ANSWER KEY” at the top right. So this is not a problem we need to solve from scratch — it’s the completed answer key.

However, since you asked me to “solve the problem accurately,” I’ll verify that the numbers follow the rules shown on the arrows. Let’s pick a few paths to check.

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Start with the first row:

Box 1: 2
Arrow to next box: +1 / 1 → 2 + 1 = 3, then ÷1 = 3 → matches box 2: 3

From 3, arrow down: + | 2 → probably means “add 2”? But wait — the symbol is “+|2”. Looking at other arrows like “+|4”, “+|6”, etc., and seeing that from 3 to 5 is +2, from 7 to 12 is +5, from 18 to 21 is +3 — it seems “+|n” actually means “add n”.

Wait — let’s look again. From 3 to 5: arrow says “+|2” → 3 + 2 = 5 ✔️
From 5 to 7: “+2” → 5 + 2 = 7 ✔️
From 7 to 12: “+|5” → 7 + 5 = 12 ✔️
From 12 to 18: “+6” → 12 + 6 = 18 ✔️
From 18 to 21: “+|3” → 18 + 3 = 21 ✔️
From 21 to 28: “+7” → 21 + 7 = 28 ✔️
From 28 to 29: “+|1” → 28 + 1 = 29 ✔️

Now check divisions:

From 9 to 12: “+3” → 9 + 3 = 12 ✔️
From 12 to 16: “+|4” → 12 + 4 = 16 ✔️
From 16 to 19: “+3” → 16 + 3 = 19 ✔️
From 19 to 25: “+|6” → 19 + 6 = 25 ✔️

Also check leftward moves:

From 5 to 8: “+3” ← but arrow points left, so maybe it’s reverse? Wait — the arrow from 8 to 5 says “+3” pointing left? That would mean 8 - 3 = 5? But the operation is labeled “+3”. Hmm.

Actually, looking carefully: the arrow from 8 to 5 has “+3” written on it, but the arrow points LEFT. So if we go from 8 to 5, we subtract 3? But the label says “+3”. That doesn’t make sense unless the operation is applied in the direction of the arrow.

Wait — perhaps the operation is always applied as written, regardless of direction? Let’s test:

If from 8 to 5, operation is “+3”, then 8 + 3 = 11 ≠ 5 → wrong.

But if we interpret the operation as what you do to get FROM the starting number TO the ending number, then:

To go from 8 to 5, you subtract 3 → but the label says “+3”. Contradiction.

Alternatively, maybe the “+3” means “add 3” to the previous number to get the next — but the arrow direction shows the flow.

Looking at the snake path: it starts at 2 → 3 → 5 → 7 → 12 → 18 → 21 → 28 → 29 → 24 → 21 → 23 → 20 → 17 → 15 → 16 → 12 → 14 → 10 → 8 → 5 → 7... wait, that loops? No, actually the snake winds through.

Perhaps better to trace the entire path in order.

Let me try to trace the snake from start to end based on arrow directions.

Start at 2 (top left)

→ right to 3 (operation: +1/1 → 2+1=3)

↓ down to 5 (operation: +|2 → 3+2=5)

← left to 8? Wait, no — from 5, there’s an arrow left to 8? But 5 to 8 is +3, and the arrow says “+3” pointing left — so if we’re going from 5 to 8, that’s +3, which matches.

But earlier I thought 8 to 5 was the move — but actually, the arrow points from 5 to 8? Let’s look at the image description.

In the user’s image description, it shows:

First row: 2 → 3 → (then below 3 is 5, with arrow down labeled +|2)

Then from 5, arrow left to 8? Or right?

Actually, in the text representation:

It says:

Row 1: 2 → 3 9 → 12 25

Then below 3: ↓ +|2 to 5

Then from 5: ← +3 to 8? Or →?

The text says: “8 ← +3 5 +2 → 7”

So from 5, arrow left to 8 with “+3”, and arrow right to 7 with “+2”.

That suggests that from 5, you can go left to 8 (by adding 3? 5+3=8) or right to 7 (5+2=7). But that would mean two paths — but it’s a snake, so probably one continuous path.

Perhaps the snake goes: 2 → 3 → 5 → 7 → 12 → 18 → 21 → 28 → 29 → 24 → 21 → 23 → 20 → 17 → 15 → 16 → 12 → 14 → 10 → 8 → 5 → ... but that revisits numbers.

This is confusing. Maybe instead of tracing the path, since this is an answer key, and all numbers are filled, and the operations are consistent when applied in the direction of the arrows, we can assume it's correct.

Let me verify a few more:

From 7 to 12: arrow down labeled “+|5” → 7 + 5 = 12 ✔️

From 12 to 18: arrow right labeled “+6” → 12 + 6 = 18 ✔️

From 18 to 21: arrow down labeled “+|3” → 18 + 3 = 21 ✔️

From 21 to 28: arrow right labeled “+7” → 21 + 7 = 28 ✔️

From 28 to 29: arrow down labeled “+|1” → 28 + 1 = 29 ✔️

From 29 to 24: arrow left labeled “+5” → 29 + 5 = 34 ≠ 24 — wait, that’s a problem.

Arrow from 29 to 24 is labeled “+5” and points left. If we go from 29 to 24, that’s subtracting 5, but the label says “+5”. Inconsistency?

Unless the operation is meant to be applied to the source to get the target, so from 29, +5 would be 34, but target is 24 — not matching.

Perhaps the arrow direction indicates the flow, and the operation is what you do to the current number to get the next.

So from 29, arrow points to 24, operation “+5” — 29 + 5 = 34 ≠ 24. Doesn't work.

Maybe it's “-5”? But it says “+5”.

Another possibility: some operations are division or subtraction, but labeled with "+" by mistake? Unlikely.

Let’s look at the bottom row:

23 ← +2 21 +3 → 24 +5 → 29

So from 21 to 23: arrow left labeled “+2” — 21 + 2 = 23 ✔️

From 21 to 24: arrow right labeled “+3” — 21 + 3 = 24 ✔️

From 24 to 29: “+5” — 24 + 5 = 29 ✔️

Now from 29 up to 28: arrow up labeled “+|1” — 29 + 1 = 30, but target is 28 — not matching.

Earlier I had from 28 to 29: “+|1” down, so 28 + 1 = 29 ✔️

Then from 29, where does it go? In the grid, 29 is at bottom right, and above it is 28, and left is 24.

The arrow from 29 to 24 is labeled “+5” and points left — but 29 + 5 = 34, not 24.

Unless the operation is “-5”, but it's written as “+5”. Perhaps it's a typo in my interpretation.

Another idea: perhaps the “+n” on a left-pointing arrow means subtract n, because you're moving left.

For example, from 29 to 24: left arrow with “+5” — if we interpret as subtract 5, then 29 - 5 = 24 ✔️

Similarly, from 8 to 5: left arrow with “+3” — 8 - 3 = 5 ✔️

From 15 to 17: left arrow with “+2” — 15 - 2 = 13, but target is 17 — not matching.

From 15 to 17: arrow left labeled “+2” — if left means subtract, 15 - 2 = 13 ≠ 17.

But 15 to 17 is +2, so if arrow points left, but operation is +2, it should be 15 + 2 = 17, so the direction might not affect the operation sign.

I think the safest way is to assume that the operation is always added to the source number to get the target number, regardless of arrow direction. So for any arrow from A to B with operation "+k", then A + k = B.

Let's test that.

From 2 to 3: +1/1 — 2 + 1 = 3, then /1 = 3 ✔️

From 3 to 5: +|2 — 3 + 2 = 5 ✔️

From 5 to 8: +3 — 5 + 3 = 8 ✔️ (arrow points left, but still 5+3=8)

From 5 to 7: +2 — 5 + 2 = 7 ✔️

From 7 to 12: +|5 — 7 + 5 = 12 ✔️

From 12 to 18: +6 — 12 + 6 = 18 ✔️

From 18 to 21: +|3 — 18 + 3 = 21 ✔️

From 21 to 28: +7 — 21 + 7 = 28 ✔️

From 28 to 29: +|1 — 28 + 1 = 29 ✔️

From 29 to 24: +5 — 29 + 5 = 34, but target is 24 — not match.

Unless it's from 24 to 29: +5 — 24 + 5 = 29 ✔️, and the arrow points from 24 to 29, not 29 to 24.

In the grid, the arrow between 24 and 29 is labeled "+5" and points from 24 to 29, so 24 + 5 = 29 ✔️

Similarly, between 21 and 24: "+3" from 21 to 24 — 21 + 3 = 24 ✔️

Between 21 and 23: "+2" from 21 to 23 — 21 + 2 = 23 ✔️

Now from 23 to 20: arrow down labeled "+|3" — 23 + 3 = 26, but target is 20 — not match.

From 20 to 23: arrow up labeled "+|3" — 20 + 3 = 23 ✔️, and arrow points up from 20 to 23.

In the grid, 20 is below 17, and 23 is to the right of 21, etc.

Let's list the connections as per the diagram:

- 2 --(+1/1)--> 3

- 3 --(+|2)--> 5

- 5 --(+3)--> 8 [left]

- 5 --(+2)--> 7 [right]

- 7 --(+|5)--> 12

- 12 --(+6)--> 18

- 18 --(+|3)--> 21

- 21 --(+7)--> 28

- 28 --(+|1)--> 29

- 24 --(+5)--> 29 [so 24 to 29]

- 21 --(+3)--> 24

- 21 --(+2)--> 23

- 20 --(+|3)--> 23 [up]

- 17 --(+3)--> 20 [down]

- 15 --(+2)--> 17 [left? 15 to 17 is +2, arrow points left from 15 to 17?]

In the text: "17 ← +2 15" so arrow from 15 to 17 labeled "+2", points left — 15 + 2 = 17 ✔️

- 15 --(+1)--> 16 [right]

- 16 --(+5)--> 21 [down]

- 12 --(+4)--> 16 [down]

- 14 --(+1)--> 15 [down]

- 10 --(+4)--> 14 [right]

- 8 --(+|2)--> 10 [down]

- 9 --(+3)--> 12 [right]

- 12 --(+|4)--> 16 [down? from 12 to 16 is +4, but 12+4=16, and arrow down]

In the grid, from 12 (middle) down to 16? But 16 is also reached from 7 down to 12, then 12 to 18, etc.

Actually, there are multiple paths, but the snake is a single path that visits each number once? Not necessarily, since some numbers appear twice? No, looking at the numbers: 2,3,5,7,8,9,10,12,14,15,16,17,18,19,20,21,23,24,25,28,29,30 — all seem unique except 12 and 21 appear in multiple places? No, in the grid, each box has a unique position, but the value 12 appears in two different boxes? Let's see:

Top row: 2,3, then 9,12,25

Second row: 8,5,7, then 16,19

Third row: 10,14, then 12,18, then 30

Fourth row: 17,15,16, then 21,28

Fifth row: 20,23,21,24,29

Oh! There are two boxes with 12: one in top row (from 9), and one in third row (from 7 and to 18).

Similarly, two boxes with 21: one in fourth row (from 18), and one in fifth row (from 16 and to 23,24).

So it's not a simple path; it's a grid with connections, and we need to ensure that for each arrow, the operation transforms the source to the target.

Let's verify all arrows:

1. 2 -> 3: +1/1 = (2+1)/1 = 3 ✔️

2. 3 -> 5: +|2 = 3+2=5 ✔️

3. 5 -> 8: +3 = 5+3=8 ✔️ (arrow left)

4. 5 -> 7: +2 = 5+2=7 ✔️ (arrow right)

5. 7 -> 12: +|5 = 7+5=12 ✔️ (arrow down)

6. 12 -> 18: +6 = 12+6=18 ✔️ (arrow right)

7. 18 -> 21: +|3 = 18+3=21 ✔️ (arrow down)

8. 21 -> 28: +7 = 21+7=28 ✔️ (arrow right)

9. 28 -> 29: +|1 = 28+1=29 ✔️ (arrow down)

10. 24 -> 29: +5 = 24+5=29 ✔️ (arrow right)

11. 21 -> 24: +3 = 21+3=24 ✔️ (arrow right) — this is the lower 21

12. 21 -> 23: +2 = 21+2=23 ✔️ (arrow left) — lower 21 to 23

13. 20 -> 23: +|3 = 20+3=23 ✔️ (arrow up)

14. 17 -> 20: +3 = 17+3=20 ✔️ (arrow down)

15. 15 -> 17: +2 = 15+2=17 ✔️ (arrow left)

16. 15 -> 16: +1 = 15+1=16 ✔️ (arrow right)

17. 16 -> 21: +5 = 16+5=21 ✔️ (arrow down) — to lower 21

18. 12 -> 16: +4 = 12+4=16 ✔️ (arrow down) — this is the middle 12 to 16

19. 14 -> 15: +1 = 14+1=15 ✔️ (arrow down)

20. 10 -> 14: +4 = 10+4=14 ✔️ (arrow right)

21. 8 -> 10: +|2 = 8+2=10 ✔️ (arrow down)

22. 9 -> 12: +3 = 9+3=12 ✔️ (arrow right) — to upper 12

23. 12 -> 16: already did, but there's also from 12 (upper) to 16? In the grid, from upper 12 (which is from 9) , arrow down to 16? But 12+4=16, and there is an arrow from 12 to 16 labeled "+|4" — yes, in second row, from 12 down to 16? Let's see the layout.

From the initial description:

After 9 -> 12, then from 12 down to 16 with "+|4"? In the text: "9 +3-> 12 +|4-> 16" but 12 to 16 is +4, and 12+4=16 ✔️

Then from 16 to 19: "+3" -> 16+3=19 ✔️

From 19 to 25: "+|6" -> 19+6=25 ✔️

From 25 to ? No outgoing, but incoming from 19.

Also, from 30: how is it reached? In third row, 30 is there, with arrow up from 28? 28 to 30: "+|2" -> 28+2=30 ✔️, and arrow up from 28 to 30.

In the grid, 28 is in fourth row, 30 in third row, so arrow up from 28 to 30 with "+|2" — 28+2=30 ✔️

And from 30, no outgoing, or to 25? 30 to 25: "-5", but arrow is from 19 to 25, and 25 to 30? Not directly connected.

In the text: "25 +|6-> 19" no, it's "16 +3-> 19 +|6-> 25" so 19 to 25 with "+|6" — 19+6=25 ✔️

Then from 25, is there an arrow to 30? In the grid, 25 is top right, 30 is middle right, so perhaps arrow down from 25 to 30? But in the text, it's not specified, but in the initial problem, it might be implied.

Looking back at user's input: in the third row, after 18, there is 30, and arrow from 28 to 30 with "+|2" up, and from 30 to 25? Not directly.

Actually, in the sequence, from 25, how to get to others? Perhaps the snake ends or branches.

But for verification, all the arrows that are drawn seem to satisfy: source + operation = target.

The only potential issue is the "/1" in "+1/1" — but since dividing by 1 does nothing, it's fine.

Also, "+|n" seems to mean "+n", as all examples work with addition.

So, the answer key is correct as given.

Since the task is to "fill in all the missing numbers", and in this image, all numbers are already filled, and it's labeled "ANSWER KEY", the final answer is the set of numbers as shown.

But for the purpose of this response, since you asked to solve the problem, and the problem is to fill in the missing numbers, but they are already filled, I think the expected output is to confirm that the numbers are correct, or perhaps to list them.

However, the instruction says: "Solve the problem accurately." and "provide the final correct answer".

Given that, and since this is an answer key, the final answer is the completed grid as shown.

But to put it in a boxed answer, perhaps list the numbers in order or something.

Since the user might expect the numbers that were missing, but in this case, none are missing — it's the key.

Perhaps for the sake of the exercise, I should provide the numbers as per the snake path.

But to keep it simple, since all calculations check out, the answer is correct.

Final Answer: The numbers in the grid are correctly filled as per the operations shown on the arrows. All transitions satisfy the given arithmetic operations. For example, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 = 8, 5 + 2 = 7, 7 + 5 = 12, and so on, up to 28 + 1 = 29, 24 + 5 = 29, etc. The answer key is accurate.

But to conform to the format, and since the problem is to fill in missing numbers, and they are all filled, I'll state that the solution is complete and correct.

Perhaps the final answer is the list of numbers in the order of the snake, but that's ambiguous.

Given the constraints, I'll box the entire grid as the answer, but that's not practical.

Another idea: perhaps the "missing numbers" were to be filled by the student, and this is the key, so for the student, the answer is the numbers provided.

So for the final answer, I'll say:

The missing numbers have been filled in correctly as shown in the answer key. Each number follows from the previous by applying the operation on the arrow. For instance, starting from 2, add 1 to get 3, add 2 to get 5, add 3 to get 8, and so on. All values are consistent with the given operations.

But to have a concise final answer, since the problem is solved, and the key is given, I'll provide the first few and last few to indicate.

I think the best is to recognize that this is the answer key, so the final answer is the set of numbers as displayed.

For the boxed answer, perhaps: \boxed{2,3,5,7,8,9,10,12,12,14,15,16,16,17,18,19,20,21,21,23,24,25,28,29,30} but that has duplicates and is messy.

Notice that in the grid, there are 25 boxes, but some numbers repeat like 12 and 21 appear twice, so total unique positions.

List all numbers in row-major order as per the grid:

Row 1: 2, 3, 9, 12, 25

Row 2: 8, 5, 7, 16, 19

Row 3: 10, 14, 12, 18, 30

Row 4: 17, 15, 16, 21, 28

Row 5: 20, 23, 21, 24, 29

So the filled numbers are: 2,3,9,12,25,8,5,7,16,19,10,14,12,18,30,17,15,16,21,28,20,23,21,24,29

And this is the answer.

Since the problem is to fill in the missing numbers, and this is the completed version, this is the solution.

So for the final answer, I'll box this list.

But to make it neat, perhaps write it as a grid.

Given the format, I'll provide the numbers in the order they appear in the grid from left to right, top to bottom.

Final Answer: \boxed{2,3,9,12,25,8,5,7,16,19,10,14,12,18,30,17,15,16,21,28,20,23,21,24,29}

But let's count: 5 rows x 5 columns = 25 numbers, yes.

And all are present.

So this should be the answer.