Autumn Worksheets - Free Printable

The Leaf Sum Game is a fun math puzzle where you need to find pairs of adjacent hexagons (shapes) on the leaf that add up to 10.

Let’s go through the steps to solve this:

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🔍 Objective:

Find all pairs of adjacent hexagons (sharing a side) whose numbers add up to 10.

We’ll scan the leaf-shaped grid and look for such pairs. Adjacent means sharing a full edge — not just touching at a corner.

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🧮 Strategy:

We'll go through each number and check its neighbors to see if any pair sums to 10.

Numbers that can make 10 with another number:
- 1 + 9 = 10
- 2 + 8 = 10
- 3 + 7 = 10
- 4 + 6 = 10
- 5 + 5 = 10

So we're looking for these combinations in adjacent cells.

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Let’s label the leaf roughly by rows from top to bottom, left to right, and identify all adjacent pairs that sum to 10.

We’ll go step by step.

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#### Row 1: Top center
- Hexagon with 3, then 8, then 7
- Check:
- 3 & 8 → 11 ✘
- 8 & 7 → 15 ✘
- No 10 here.

But wait — let's map it more carefully.

Actually, the layout is like a honeycomb pattern. Let's trace it systematically.

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Let’s list the numbers in order, row by row, and check adjacency.

Here’s the structure (with positions labeled):

```
Row 1: [3] [8] [7]
Row 2: [9] [1] [3] [2] [7]
Row 3: [4] [3] [2] [7] [1] [9] [8]
Row 4: [9] [5] [4] [1] [6] [7] [5] [3] [2]
Row 5: [5] [4] [1] [2] [3] [1] [9] [8]
Row 6: [2] [1] [2] [1] [9] [8]
Row 7: [6] [4] [3] [8] [7]
Row 8: [7] [1] [9]
```

Now we’ll check adjacent pairs (sharing an edge) that sum to 10.

We’ll go through each cell and check its neighbors.

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Step-by-step Search:

#### Start from top:
- 3 (top): neighbors are 8 and 1? Wait — need to visualize connections.

Let’s instead go by position.

Let me reconstruct the grid as a honeycomb lattice.

But since I can’t draw, I’ll use relative positions.

Let’s go through known pairs.

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✔ Look for 1+9 pairs:

Look for 1s and 9s near each other.

- In row 2: 9 (left), 1 (middle) → 9 and 1 → sum = 10 → YES! They are adjacent.
- So (9,1) in row 2 → pair found

- In row 4: 9 (left), 5, 4, 1, ... → 9 is at far left, next is 5 → no 1 adjacent?
- But later: [1] at position 4, then [6], then [7], then [5], then [3], then [2]
- Any 1 next to 9? No.

Wait — in row 4: we have:
- [9], [5], [4], [1], [6], [7], [5], [3], [2]

Is there a 9 next to a 1? The 9 is at the start, then 5 → not adjacent to 1.

But earlier in row 2: 9 and 1 are adjacent → YES!

Also, in row 4, we have a 1 and a 9?

Wait — look at row 5: [5], [4], [1], [2], [3], [1], [9], [8]

- [1] and [9] → are they adjacent? Yes! The last two: 1 and 9 → sum = 10 → YES!
- So (1,9) in row 5 → pair found

Also, [9] and [8] → 17 → no

But earlier: [1] and [9] → yes → pair

Also, in row 6: [2], [1], [2], [1], [9], [8]
- [1] and [9] → adjacent → YES → (1,9) → pair

So we have:
- Row 2: 9 and 1 → (9,1)
- Row 5: 1 and 9 → (1,9)
- Row 6: 1 and 9 → (1,9)

Are these distinct pairs? Yes.

Now, (2,8) pairs?

Look for 2 and 8 adjacent.

- Row 1: 7, 8, 3 → 8 and 7 → 15; 8 and 3 → 11 → no
- Row 2: 9,1,3,2,7 → 2 and 7 → 9; 3 and 2 → 5 → no
- Row 3: 4,3,2,7,1,9,8 → check:
- 2 and 7 → 9
- 7 and 1 → 8
- 1 and 9 → 10 → YES! Already counted above
- 9 and 8 → 17 → no
- Row 4: 9,5,4,1,6,7,5,3,2
- 2 at end → neighbor is 3 → 5 → no
- Row 5: 5,4,1,2,3,1,9,8
- 2 and 3 → 5
- 3 and 1 → 4
- 1 and 9 → 10 → already found
- Row 6: 2,1,2,1,9,8
- 2 and 1 → 3
- 1 and 2 → 3
- 2 and 1 → 3
- 1 and 9 → 10 → already found
- 9 and 8 → 17
- Row 7: 6,4,3,8,7
- 3 and 8 → 11
- 8 and 7 → 15
- Row 8: 7,1,9
- 7 and 1 → 8
- 1 and 9 → 10 → YES! (1,9) → new one?

Wait — row 8: [7], [1], [9]

- 1 and 9 → adjacent → YES → sum = 10 → another (1,9)

So now we have multiple (1,9) pairs.

But also, is there a (2,8)?

Check row 7: [6], [4], [3], [8], [7]

- 3 and 8 → 11
- 8 and 7 → 15 → no

But row 3: [4], [3], [2], [7], [1], [9], [8]

- 2 and 7 → 9
- 7 and 1 → 8
- 1 and 9 → 10 → yes
- 9 and 8 → 17

No 2 and 8 adjacent.

But what about row 4: [9], [5], [4], [1], [6], [7], [5], [3], [2]

- 3 and 2 → 5 → no

Wait — row 7: [6], [4], [3], [8], [7]

- 3 and 8 → 11 → no

But row 6: [2], [1], [2], [1], [9], [8]

- 8 has neighbors: 9 and ? → 9 and 8 → 17 → no
- 2 and 1 → 3 → no

Wait — row 5: [5], [4], [1], [2], [3], [1], [9], [8]

- 8 is at end → neighbor is 9 → 17 → no

But row 4: last few: [5], [3], [2] → 3 and 2 → 5

Still no 2 and 8.

What about (3,7)?

Look for 3 and 7 adjacent.

- Row 1: 3,8,7 → 3 and 8 → 11; 8 and 7 → 15 → no
- Row 2: 9,1,3,2,7 → 3 and 2 → 5; 2 and 7 → 9 → no
- Row 3: 4,3,2,7,... → 3 and 2 → 5; 2 and 7 → 9 → no
- Row 4: 9,5,4,1,6,7,5,3,2 → 7 and 5 → 12; 5 and 3 → 8; 3 and 2 → 5 → no
- Row 5: 5,4,1,2,3,1,9,8 → 3 and 1 → 4 → no
- Row 6: 2,1,2,1,9,8 → no 3 or 7
- Row 7: 6,4,3,8,7 → 3 and 8 → 11; 8 and 7 → 15 → no
- Row 8: 7,1,9 → 7 and 1 → 8 → no

No (3,7) pairs.

How about (4,6)?

Look for 4 and 6 adjacent.

- Row 4: [4], [1], [6] → 4 and 1 → 5; 1 and 6 → 7 → no
- Row 3: [4], [3], [2],... → 4 and 3 → 7 → no
- Row 4: [6] and [7] → 13 → no
- Row 5: [4] and [1] → 5 → no
- Row 7: [4] and [3] → 7 → no

No 4 and 6 adjacent.

What about (5,5)?

Any two 5s adjacent?

- Row 4: [5], [4], [1], [6], [7], [5], ... → 5 and 4 → 9; 5 and 7 → 12 → no
- Row 4: two 5s? [5], ..., [5] → are they adjacent? No — separated by 7 → not adjacent
- Row 5: [5], [4], ... → 5 and 4 → 9 → no

No (5,5) pairs.

So only valid pairs are those that sum to 10 via (1,9), (2,8), (3,7), (4,6), (5,5)

We’ve found:

✔ Found Pairs:

1. Row 2: 9 and 1 → (9,1) → sum = 10
2. Row 5: 1 and 9 → (1,9) → sum = 10
3. Row 6: 1 and 9 → (1,9) → sum = 10
4. Row 8: 1 and 9 → (1,9) → sum = 10

Wait — but are these distinct adjacent pairs?

Let’s locate them precisely.

But perhaps we missed some.

Wait — row 4: [9], [5], [4], [1], [6], [7], [5], [3], [2]

- 9 and 5 → 14 → no
- 5 and 4 → 9 → no
- 4 and 1 → 5 → no
- 1 and 6 → 7 → no
- 6 and 7 → 13 → no
- 7 and 5 → 12 → no
- 5 and 3 → 8 → no
- 3 and 2 → 5 → no

No 10 here.

But row 3: [4], [3], [2], [7], [1], [9], [8]

- 2 and 7 → 9
- 7 and 1 → 8
- 1 and 9 → 10 → YES → (1,9) → another one!

So now we have:
- Row 3: 1 and 9 → YES

And row 4: [1] and [6] → no

But row 5: [1] and [9] → YES

Row 6: [1] and [9] → YES

Row 8: [1] and [9] → YES

So how many (1,9) pairs?

Let’s count:

1. Row 2: 9 and 1 → YES (first)
2. Row 3: 1 and 9 → YES (second)
3. Row 5: 1 and 9 → YES (third)
4. Row 6: 1 and 9 → YES (fourth)
5. Row 8: 1 and 9 → YES (fifth)

Are all these adjacent?

Let’s confirm:

- Row 2: [9], [1], [3], [2], [7] → 9 and 1 are adjacent → YES
- Row 3: [...], [1], [9], [8] → 1 and 9 adjacent → YES
- Row 5: [...], [1], [9], [8] → 1 and 9 adjacent → YES
- Row 6: [...], [1], [9], [8] → 1 and 9 adjacent → YES
- Row 8: [7], [1], [9] → 1 and 9 adjacent → YES

So five (1,9) pairs.

Now, are there any others?

What about (2,8)?

Look for 2 and 8 adjacent.

- Row 3: [2], [7], [1], [9], [8] → 2 and 7 → 9; 7 and 1 → 8; 1 and 9 → 10; 9 and 8 → 17 → no
- Row 4: [2] at end → neighbor is 3 → 5 → no
- Row 5: [2] → neighbors: 3 and 1 → 5 → no
- Row 6: [2] → neighbors: 1 and 2 → 3 → no
- Row 7: [8] → neighbors: 3 and 7 → 11 and 15 → no
- Row 4: [8]? No — row 4 ends with 2
- Row 3: [8] at end → neighbors: 9 and ? → 9 and 8 → 17 → no

No (2,8)

What about (3,7)?

- Row 1: 3 and 8 → 11; 8 and 7 → 15 → no
- Row 2: 3 and 2 → 5 → no
- Row 3: 3 and 2 → 5 → no
- Row 4: 3 and 2 → 5 → no
- Row 7: 3 and 8 → 11 → no

No

(4,6)?

- Row 4: [4], [1], [6] → 4 and 1 → 5; 1 and 6 → 7 → no
- Row 3: [4], [3], [2] → 4 and 3 → 7 → no
- Row 7: [4], [3], [8] → 4 and 3 → 7 → no

No

(5,5)?

- Row 4: [5], ..., [5] → are they adjacent? No — separated by 7 → not adjacent → no

So only possible pairs are (1,9)

Wait — but what about (9,1) and (1,9) — same thing.

So total of 5 pairs of adjacent numbers that sum to 10.

But let’s double-check if any other pair exists.

Wait — row 7: [6], [4], [3], [8], [7]

- 3 and 8 → 11
- 8 and 7 → 15
- 6 and 4 → 10 → YES! (6,4) → sum = 10 → YES!

Oh! We missed this!

- 6 and 4 → 10 → YES

Are they adjacent? Yes — in row 7: [6], [4], [3], [8], [7]

So 6 and 4 are adjacent → sum = 10 → new pair

Similarly, (4,6) → same thing.

So now we have:

6. Row 7: 6 and 4 → (6,4) → sum = 10

Also, check if (7,3)?

- 3 and 8 → 11 → no
- 7 and 8 → 15 → no

But (3,7)?

- 3 and 8 → 11 → no

Wait — row 7: [3] and [8] → 11 → no

But (6,4) is confirmed.

Now, are there more?

What about (8,2)?

- Row 3: [8] → neighbors: 9 and ? → 9 and 8 → 17 → no
- Row 6: [8] → neighbors: 9 and ? → 9 and 8 → 17 → no
- Row 5: [8] → neighbors: 9 → 17 → no
- Row 7: [8] → neighbors: 3 and 7 → 11 and 15 → no

No

What about (7,3)?

- Row 1: 7 and 8 → 15 → no
- Row 2: 7 and 2 → 9 → no
- Row 4: 7 and 5 → 12 → no
- Row 7: 7 and 8 → 15 → no

No

But wait — row 4: [7] and [5] → 12 → no

So only:

✔ (1,9) pairs:
1. Row 2: 9 and 1
2. Row 3: 1 and 9
3. Row 5: 1 and 9
4. Row 6: 1 and 9
5. Row 8: 1 and 9

✔ (6,4) pair:
6. Row 7: 6 and 4

Wait — is there a (4,6) elsewhere?

Row 4: [4], [1], [6] → 4 and 1 → 5; 1 and 6 → 7 → no

Only one (6,4)

Now, what about (7,3)?

No.

Wait — row 4: [5], [3], [2] → 3 and 2 → 5 → no

Another idea: (8,2)?

No.

Wait — row 4: [3] and [2] → 5 → no

But row 7: [4] and [3] → 7 → no

So total of 6 pairs?

But let’s verify each one:

1. Row 2: [9] and [1] → adjacent → 9+1=10 → ✔
2. Row 3: [1] and [9] → adjacent → 1+9=10 → ✔
3. Row 5: [1] and [9] → adjacent → 1+9=10 → ✔
4. Row 6: [1] and [9] → adjacent → 1+9=10 → ✔
5. Row 8: [1] and [9] → adjacent → 1+9=10 → ✔
6. Row 7: [6] and [4] → adjacent → 6+4=10 → ✔

Are there any more?

Wait — row 4: [5], [4], [1], [6], [7], [5], [3], [2]

- [4] and [1] → 5 → no
- [1] and [6] → 7 → no
- [6] and [7] → 13 → no

No

Row 5: [5], [4], [1], [2], [3], [1], [9], [8]

- [4] and [1] → 5 → no
- [1] and [2] → 3 → no
- [2] and [3] → 5 → no
- [3] and [1] → 4 → no
- [1] and [9] → 10 → already counted

Row 6: [2], [1], [2], [1], [9], [8]

- [1] and [9] → 10 → already counted

Row 7: [6], [4], [3], [8], [7]

- [6] and [4] → 10 → ✔
- [4] and [3] → 7 → no
- [3] and [8] → 11 → no
- [8] and [7] → 15 → no

Row 8: [7], [1], [9]

- [7] and [1] → 8 → no
- [1] and [9] → 10 → ✔

So total 6 pairs.

But wait — is (6,4) really adjacent?

Yes — in row 7: [6], [4], [3], [8], [7]

So 6 and 4 share an edge → YES

So final answer:

✔ Solution: There are 6 pairs of adjacent numbers that add to 10.

They are:

1. 9 and 1 in row 2
2. 1 and 9 in row 3
3. 1 and 9 in row 5
4. 1 and 9 in row 6
5. 1 and 9 in row 8
6. 6 and 4 in row 7

Note: All are adjacent (share a side).

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✔ Final Answer:

There are 6 pairs of adjacent hexagons that add up to 10.

These pairs are:
- (9,1) – row 2
- (1,9) – row 3
- (1,9) – row 5
- (1,9) – row 6
- (1,9) – row 8
- (6,4) – row 7

You can circle or highlight these pairs on the leaf.

Let me know if you'd like a visual guide!