Write the missing numbers in the train carriages.

Let’s solve each train one by one. We’re looking for the missing numbers in order — like counting up by 1s, or maybe another pattern.

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First Train:
Cars show:
Purple: 1
Blue: ?
Red: ?
Yellow: 4
Purple: ?

We know it starts at 1 and goes to 4 in the yellow car (which is the 4th car). So let’s count:

Car 1 (purple): 1
Car 2 (blue): should be 2
Car 3 (red): should be 3
Car 4 (yellow): 4 ✔
Car 5 (purple): should be 5

So first train missing numbers: 2, 3, 5

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Second Train:
Cars show:
Purple: ?
Blue: ?
Red: 8
Yellow: 9
Purple: ?

If red is 8 and yellow is 9, then they are consecutive. That means we’re counting up by 1s again.

So before 8 comes 7, then 6.

Car 1 (purple): 6
Car 2 (blue): 7
Car 3 (red): 8 ✔
Car 4 (yellow): 9 ✔
Car 5 (purple): 10

Missing numbers: 6, 7, 10

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Third Train:
Cars show:
Purple: ?
Blue: 12
Red: ?
Yellow: ?
Purple: 15

We have 12 in blue (car 2) and 15 in purple (car 5). Let’s see how many steps from car 2 to car 5: that’s 3 steps (car 3, 4, 5).

From 12 to 15 is +3 over 3 cars → so each car increases by 1.

So:

Car 1 (purple): 11
Car 2 (blue): 12 ✔
Car 3 (red): 13
Car 4 (yellow): 14
Car 5 (purple): 15 ✔

Missing numbers: 11, 13, 14

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Fourth Train:
Cars show:
Purple: ?
Blue: ?
Red: 18
Yellow: ?
Purple: ?

Only 18 is given — in the red car, which is car 3.

Assuming same pattern — counting up by 1s — then:

Car 1 (purple): 16
Car 2 (blue): 17
Car 3 (red): 18 ✔
Car 4 (yellow): 19
Car 5 (purple): 20

Missing numbers: 16, 17, 19, 20

Wait — actually, only 3 blanks? Let me check:

Looking back at image description: fourth train has 5 cars, with only red (car 3) showing 18. The rest are blank. So yes, 4 missing numbers? But in previous trains, sometimes 3 blanks, sometimes more.

Actually, looking at structure:

Each train has 5 cars after engine. In fourth train:

- Car 1: blank
- Car 2: blank
- Car 3: 18
- Car 4: blank
- Car 5: blank

That’s 4 blanks. But in our answer format, we’ll list all missing ones.

But wait — let’s double-check if pattern is always +1.

In third train: 11,12,13,14,15 → perfect +1.

Second train: 6,7,8,9,10 → +1.

First train: 1,2,3,4,5 → +1.

So fourth train must also be +1.

So if car 3 = 18, then:

Car 1 = 16
Car 2 = 17
Car 4 = 19
Car 5 = 20

Yes.

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Now, compiling all answers per train:

Train 1 missing: 2, 3, 5
Train 2 missing: 6, 7, 10
Train 3 missing: 11, 13, 14
Train 4 missing: 16, 17, 19, 20

But wait — in the original problem, each train has exactly 3 white circles (missing numbers)? Let me recheck based on typical worksheet design.

Actually, looking at user's image description:

First train: positions 2,3,5 missing → 3 blanks
Second train: positions 1,2,5 missing → 3 blanks
Third train: positions 1,3,4 missing → 3 blanks
Fourth train: positions 1,2,4,5 missing → 4 blanks? Hmm.

Wait — perhaps I miscounted.

Let me label each train’s cars as C1 to C5 (left to right after engine):

Train 1:
C1: 1
C2: ?
C3: ?
C4: 4
C5: ?
→ Missing: C2, C3, C5 → 3 numbers

Train 2:
C1: ?
C2: ?
C3: 8
C4: 9
C5: ?
→ Missing: C1, C2, C5 → 3 numbers

Train 3:
C1: ?
C2: 12
C3: ?
C4: ?
C5: 15
→ Missing: C1, C3, C4 → 3 numbers

Train 4:
C1: ?
C2: ?
C3: 18
C4: ?
C5: ?
→ Missing: C1, C2, C4, C5 → 4 numbers? But that breaks pattern.

Wait — maybe in Train 4, it’s still 3 missing? Or perhaps I made a mistake.

Alternatively, maybe the pattern isn’t always starting from beginning — but no, all others are sequential.

Perhaps in Train 4, since only C3=18 is given, and assuming sequence continues, we fill all blanks.

But to match expected output, let’s assume each train expects 3 missing numbers? No — visually, Train 4 has 4 blanks.

But in the initial problem statement, it says “write the missing numbers” — plural — doesn’t specify how many per train.

So we’ll go with what fits the pattern.

Final decision: All trains follow consecutive counting (+1), so:

Train 1: 1, _, _, 4, _ → fills to 1,2,3,4,5 → missing: 2,3,5
Train 2: _, _, 8,9,_ → fills to 6,7,8,9,10 → missing: 6,7,10
Train 3: _,12,_,_,15 → fills to 11,12,13,14,15 → missing: 11,13,14
Train 4: _,_,18,_,_ → fills to 16,17,18,19,20 → missing: 16,17,19,20

But since the question likely expects listing per train, and possibly in order left to right, we’ll present them as such.

However, to avoid confusion, let’s write the full completed sequences and extract missing values in order of appearance.

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After careful checking, here are the missing numbers for each train, in the order they appear from left to right:

Train 1: 2, 3, 5
Train 2: 6, 7, 10
Train 3: 11, 13, 14
Train 4: 16, 17, 19, 20

But wait — in Train 4, if we list missing in order: C1, C2, C4, C5 → 16,17,19,20 — that’s correct.

However, some worksheets might expect only 3 per train — but based on logic, this is accurate.

Alternatively, maybe Train 4 is different? Let’s test if it could be something else.

Suppose Train 4: if C3=18, and maybe it’s counting by 2s? Then C1=14, C2=16, C4=20, C5=22 — but then C5 would be 22, but no constraint. However, all other trains are +1, so unlikely.

Stick with +1.

Thus, final answers per train:

Train 1: 2, 3, 5
Train 2: 6, 7, 10
Train 3: 11, 13, 14
Train 4: 16, 17, 19, 20

But to present cleanly, perhaps list all missing numbers in order across all trains? No, better per train.

Since the problem says “write the missing numbers” without specifying grouping, but visually grouped by train, we’ll group by train.

Final Answer will list them train by train.

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Final Answer:
Train 1: 2, 3, 5
Train 2: 6, 7, 10
Train 3: 11, 13, 14
Train 4: 16, 17, 19, 20