1st Grade Math Games - Free Printable
Educational worksheet: 1st Grade Math Games. Download and print for classroom or home learning activities.
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Step-by-step solution for: 1st Grade Math Games
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Show Answer Key & Explanations
Step-by-step solution for: 1st Grade Math Games
This is a fun math puzzle called "Race to the Moon", where the goal is to solve addition and subtraction problems (up to 10) and find a path from Earth to the Moon by moving through hexagons with correct answers.
---
- The board is made of hexagonal tiles, each containing an addition or subtraction problem.
- You start at Earth (on the left) and must reach the Moon (on the right).
- You can only move through hexagons whose answer equals a number on the top row (from 0 to 20).
- But here’s the twist: You're not told which numbers are allowed.
- However, since the title says "Adding and Subtracting to 10", it's likely that only results from 0 to 10 are valid for the path.
But wait — let’s look carefully.
There's a number line at the top:
`0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20`
And yellow hexagons seem to highlight certain problems. But not all yellow ones are necessarily correct — they may just be visual cues.
Wait — actually, in many versions of this game, you can only step on tiles where the result is ≤ 10, or maybe you have to follow a path where each step adds up to a specific total.
But in this version, the goal is to find a continuous path from Earth to the Moon, moving through adjacent hexagons, such that each tile's result is between 0 and 10 inclusive — because the game is "adding and subtracting to 10".
Let’s analyze:
---
1. Calculate the result of every expression in the hexagons.
2. Only allow movement through hexagons where the result is ≤ 10 (since the title says "to 10").
- But some expressions give results > 10, like:
- `9+4 = 13`
- `10+3 = 13`
- `8+9 = 17`
- `6+10 = 16`
- etc.
- So if we restrict to answers ≤ 10, those are invalid.
But notice: some yellow tiles have answers over 10, so maybe the rule isn't that strict.
Wait — perhaps the yellow tiles are the only ones you can use?
Let’s check that idea.
---
In the image:
- Yellow tiles are highlighted.
- White tiles are not.
So perhaps:
> You can only move on yellow tiles.
Let’s test that.
---
Let’s go through each yellow hexagon and compute its value:
```
Top row (left to right):
6-1 = 5
9+4 = 13 → ✘ too big? but yellow
7-5 = 2
10-2 = 8
Next row:
8+2 = 10
7+2 = 9
6+5 = 11 → ✘
9-0 = 9
10-5 = 5
Next:
9+3 = 12 → ✘
8-1 = 7
9-4 = 5
6-5 = 1
10+3 = 13 → ✘
Next:
7+0 = 7
3+5 = 8
8+5 = 13 → ✘
3+6 = 9
6+7 = 13 → ✘
Next:
7+3 = 10
6+6 = 12 → ✘
7+7 = 14 → ✘
8-7 = 1
6+7 = 13 → ✘
Next:
6-2 = 4
9-3 = 6
5+4 = 9
3+8 = 11 → ✘
10-5 = 5
Next:
9+4 = 13 → ✘
7-4 = 3
5+6 = 11 → ✘
6+9 = 15 → ✘
9-2 = 7
Next:
6-1 = 5
5-5 = 0
1+8 = 9
7-6 = 1
8+9 = 17 → ✘
Next:
5-2 = 3
6+4 = 10
6+6 = 12 → ✘
9+9 = 18 → ✘
6+10 = 16 → ✘
Next:
5+7 = 12 → ✘
6+8 = 14 → ✘
8-3 = 5
7+8 = 15 → ✘
9-8 = 1
Next:
3-2 = 1
7-5 = 2
9-5 = 4
```
Now, list all yellow tiles with their values:
| Expression | Result |
|-----------|--------|
| 6-1 | 5 |
| 9+4 | 13 |
| 7-5 | 2 |
| 10-2 | 8 |
| 8+2 | 10 |
| 7+2 | 9 |
| 6+5 | 11 |
| 9-0 | 9 |
| 10-5 | 5 |
| 9+3 | 12 |
| 8-1 | 7 |
| 9-4 | 5 |
| 6-5 | 1 |
| 10+3 | 13 |
| 7+0 | 7 |
| 3+5 | 8 |
| 8+5 | 13 |
| 3+6 | 9 |
| 6+7 | 13 |
| 7+3 | 10 |
| 6+6 | 12 |
| 7+7 | 14 |
| 8-7 | 1 |
| 6+7 | 13 |
| 6-2 | 4 |
| 9-3 | 6 |
| 5+4 | 9 |
| 3+8 | 11 |
| 10-5 | 5 |
| 9+4 | 13 |
| 7-4 | 3 |
| 5+6 | 11 |
| 6+9 | 15 |
| 9-2 | 7 |
| 6-1 | 5 |
| 5-5 | 0 |
| 1+8 | 9 |
| 7-6 | 1 |
| 8+9 | 17 |
| 5-2 | 3 |
| 6+4 | 10 |
| 6+6 | 12 |
| 9+9 | 18 |
| 6+10 | 16 |
| 5+7 | 12 |
| 6+8 | 14 |
| 8-3 | 5 |
| 7+8 | 15 |
| 9-8 | 1 |
| 3-2 | 1 |
| 7-5 | 2 |
| 9-5 | 4 |
Now, filter out any yellow tile with result > 10 (since the game is "to 10"):
Valid yellow tiles (result ≤ 10):
| Expression | Result |
|----------|--------|
| 6-1 | 5 |
| 7-5 | 2 |
| 10-2 | 8 |
| 8+2 | 10 |
| 7+2 | 9 |
| 9-0 | 9 |
| 10-5 | 5 |
| 8-1 | 7 |
| 9-4 | 5 |
| 6-5 | 1 |
| 7+0 | 7 |
| 3+5 | 8 |
| 3+6 | 9 |
| 7+3 | 10 |
| 6-2 | 4 |
| 9-3 | 6 |
| 5+4 | 9 |
| 10-5 | 5 |
| 7-4 | 3 |
| 9-2 | 7 |
| 6-1 | 5 |
| 5-5 | 0 |
| 1+8 | 9 |
| 7-6 | 1 |
| 5-2 | 3 |
| 6+4 | 10 |
| 8-3 | 5 |
| 9-8 | 1 |
| 3-2 | 1 |
| 7-5 | 2 |
| 9-5 | 4 |
We now need to find a continuous path from Earth (left side) to Moon (right side) using only these yellow tiles with answers ≤ 10.
Let’s try to trace a possible path.
---
Start near Earth (left edge).
Look at the first column (leftmost):
- 8+2 = 10 ✔ (yellow)
- 2-2 = 0 ✘ (white) → skip
- 7+3 = 10 ✔
- 9+4 = 13 ✘ (too big)
- 6-1 = 5 ✔
- 5+7 = 12 ✘
- 3-2 = 1 ✔
So valid yellow tiles on the left:
- 8+2 = 10 (top-left)
- 7+3 = 10
- 6-1 = 5
- 3-2 = 1
Now, from 8+2 = 10, neighbors:
- Right: 9+3 = 12 ✘ (invalid)
- Down-right: 9+3 = 12 ✘
- Down: 7+3 = 10 ✔
- Down-left: 2-2 = 0 ✘
So from 8+2 → down to 7+3 = 10 ✔
From 7+3 → neighbors:
- Right: 6-2 = 4 ✔
- Down-right: 9+4 = 13 ✘
- Down: 6-1 = 5 ✔
- Down-left: 7+0 = 7 ✔
So multiple options.
Let’s try:
Path attempt:
1. 8+2 = 10 (start)
2. ↓ to 7+3 = 10
3. ↓ to 6-1 = 5
4. → to 5-5 = 0? Wait, 5-5 is white, but 5-5 is not yellow → cannot use.
Wait — 5-5 is white, so even though result is 0, it's not yellow → invalid.
But 6-1 = 5 is yellow, and its neighbors:
- Up: 7+3 = 10 ✔
- Right: 7+4 = 11 ✘ (white)
- Down: 5-2 = 3 ✔ (yellow!)
- Down-left: 5+7 = 12 ✘
So from 6-1 = 5 → down to 5-2 = 3
Then from 5-2 = 3 → neighbors:
- Right: 6+8 = 14 ✘
- Down: 6+9 = 15 ✘
- Down-right: 7-5 = 2 ✔ (yellow)
So → 7-5 = 2
Then from 7-5 = 2 → right to 8-3 = 5 ✔
→ 8-3 = 5
Then → right to 9-5 = 4 ✔
→ 9-5 = 4
Then → right to 7+8 = 15 ✘
Or down? No.
Wait — 9-5 = 4 has neighbor:
- Up-right: 6+4 = 10 ✔
But 6+4 = 10 is above it.
Wait — let’s map positions better.
Instead, let’s try another route.
---
Let’s consider a central path.
Start from 8+2 = 10 → down to 7+3 = 10
→ down to 6-1 = 5
→ down to 5-2 = 3
→ down to 7-5 = 2
→ right to 8-3 = 5
→ right to 9-5 = 4
→ right to 7+8 = 15 ✘
No.
Wait — 8-3 = 5 has other neighbors?
- Up: 6+8 = 14 ✘
- Up-right: 6+4 = 10 ✔
Yes! 6+4 = 10 is yellow and adjacent.
So from 8-3 = 5 → up-right to 6+4 = 10
Then from 6+4 = 10 → up to 5+6 = 11 ✘
→ right to 6+6 = 12 ✘
→ down to 8-3 = 5 already visited
→ down-right: 7+8 = 15 ✘
→ up-left: 5-5 = 0 ✘ (white)
Not helpful.
Alternative path:
Try starting from 3-2 = 1 (bottom-left)
→ up to 6-1 = 5 ✔
→ up to 7+3 = 10 ✔
→ up to 8+2 = 10 ✔
Then → right to 9+3 = 12 ✘
→ down to 7+0 = 7 ✔
→ down to 6+6 = 12 ✘
→ right to 8-1 = 7 ✔
→ right to 9-4 = 5 ✔
→ right to 8+5 = 13 ✘
→ down to 7+7 = 14 ✘
→ down-right: 8-7 = 1 ✔
→ right to 3+6 = 9 ✔
→ right to 6+7 = 13 ✘
→ down to 9-2 = 7 ✔
→ right to 10-5 = 5 ✔
→ right to 10-5 = 5 again? Wait.
Wait — 10-5 = 5 appears twice.
One is at top-right, one is lower.
Let’s look at 10-5 = 5 (lower right):
It is adjacent to 9-2 = 7, and then to 8+9 = 17 ✘
But 10-5 = 5 is yellow, and its neighbors:
- Left: 9-2 = 7 ✔
- Up: 3+8 = 11 ✘
- Down: 8+9 = 17 ✘
- Down-right: 6+10 = 16 ✘
So no way to go further.
But earlier we had 9-4 = 5, then 8-7 = 1, then 3+6 = 9, then 9-2 = 7, then 10-5 = 5
Can we go from 10-5 = 5 to 10-2 = 8? Are they adjacent?
Let’s check layout.
Looking at the grid:
Top row:
- 6-1 (5), 9+4 (13), 7-5 (2), 10-2 (8)
Then below:
- 8+2 (10), 7+2 (9), 6+5 (11), 9-0 (9), 10-5 (5)
So 10-2 = 8 is at top-right, 10-5 = 5 is below it.
Are they adjacent? Yes — vertically.
So 10-2 = 8 → down to 10-5 = 5
Then from 10-5 = 5 → down to 10+3 = 13 ✘
→ left to 9-0 = 9 ✔
→ left to 6+5 = 11 ✘
→ down to 6-5 = 1 ✔
→ down to 10+3 = 13 ✘
→ down to 6+7 = 13 ✘
Not working.
Wait — what about 9-0 = 9?
It's yellow, result 9.
Neighbors:
- Up: 7-5 = 2 ✔
- Down: 9-4 = 5 ✔
- Left: 6+5 = 11 ✘
- Right: 10-5 = 5 ✔
So yes, 9-0 = 9 is connected.
But how to get from left to right?
Let’s try this path:
Start at 8+2 = 10 (left-top)
→ down to 7+3 = 10
→ down to 6-1 = 5
→ down to 5-2 = 3
→ down to 7-5 = 2
→ right to 8-3 = 5
→ up-right to 6+4 = 10
→ right to 7+8 = 15 ✘
No.
Wait — 8-3 = 5 → right to 9-5 = 4 ✔
→ right to 7+8 = 15 ✘
→ up to 6+8 = 14 ✘
→ down to 6+9 = 15 ✘
Dead end.
Alternative: from 9-4 = 5 → right to 8+5 = 13 ✘
→ down to 8-7 = 1 ✔
→ right to 3+6 = 9 ✔
→ right to 6+7 = 13 ✘
→ down to 9-2 = 7 ✔
→ right to 10-5 = 5 ✔
→ right to 8+9 = 17 ✘
→ down to 6+10 = 16 ✘
Still stuck.
But 10-5 = 5 is near the Moon.
Is there a way to reach 10-2 = 8?
Yes — from 9-0 = 9 → up to 7-5 = 2 → up to 9+4 = 13 ✘
No.
Wait — 10-2 = 8 is at top-right.
Its neighbors:
- Left: 7-5 = 2 ✔
- Down: 10-5 = 5 ✔
- Down-left: 9-0 = 9 ✔
So from 10-2 = 8, we can go to 10-5 = 5 or 9-0 = 9
But to get to 10-2 = 8, we need to come from left.
Can we reach 7-5 = 2 from the center?
Yes — 7-5 = 2 is yellow.
Its neighbors:
- Up: 9+4 = 13 ✘
- Down: 6-5 = 1 ✔
- Left: 6+5 = 11 ✘
- Right: 10-2 = 8 ✔
So only way to enter 7-5 = 2 is from 6-5 = 1
And 6-5 = 1 is yellow.
Its neighbors:
- Up: 4+7 = 11 ✘
- Down: 6-5 = 1 → same
- Left: 9-4 = 5 ✔
- Right: 6-5 = 1 → same
- Down-left: 6-5 = 1 → no
Wait — 6-5 = 1 is surrounded by:
- Up: 4+7 = 11 ✘
- Down: 6-5 = 1 → same tile
- Left: 9-4 = 5 ✔
- Right: 6-5 = 1 → same
- Up-left: 6+5 = 11 ✘
- Down-right: 6-5 = 1 → same
So only connection is to 9-4 = 5
So path:
9-4 = 5 → right to 6-5 = 1 → up to 7-5 = 2 → right to 10-2 = 8
Then from 10-2 = 8 → down to 10-5 = 5 → down to 10+3 = 13 ✘
But 10-5 = 5 is also connected to 9-0 = 9 → left to 6+5 = 11 ✘
No way to continue.
But wait — 10-5 = 5 is also connected to 9-0 = 9, which is connected to 9-4 = 5, which is connected to 8-1 = 7, which is connected to 7+2 = 9, which is connected to 8+2 = 10, which is on the left.
So we can make a loop, but not a clear path from left to right.
Perhaps the intended path is to go through the center.
Let’s try:
Start: 8+2 = 10 → down to 7+3 = 10 → down to 6-1 = 5 → down to 5-2 = 3 → down to 7-5 = 2 → right to 8-3 = 5 → right to 9-5 = 4 → right to 7+8 = 15 ✘
No.
Another idea: 6+4 = 10 is yellow.
Its neighbors:
- Up: 5+6 = 11 ✘
- Down: 8-3 = 5 ✔
- Left: 5-5 = 0 ✘
- Right: 6+6 = 12 ✘
- Up-right: 6+8 = 14 ✘
- Down-right: 7+8 = 15 ✘
Only connected to 8-3 = 5
Which is connected to 7-5 = 2, etc.
Still no.
Wait — what about 3-2 = 1 → up to 6-1 = 5 → up to 7+3 = 10 → up to 8+2 = 10 → right to 9+3 = 12 ✘
No.
Perhaps the only viable path is through the middle row.
Let’s try:
Start at 8+2 = 10 → down to 7+3 = 10 → down to 6-1 = 5 → down to 5-2 = 3 → down to 7-5 = 2 → right to 8-3 = 5 → up-right to 6+4 = 10 → right to 7+8 = 15 ✘
No.
Alternatively, from 8-3 = 5 → down to 6+9 = 15 ✘
All dead ends.
But wait — 9-5 = 4 → down to 9-8 = 1 ✔
→ right to 9-8 = 1 → down to 9-8 = 1 → no
9-8 = 1 is at bottom-right.
Its neighbors:
- Left: 7-5 = 2 ✔
- Up: 7+8 = 15 ✘
- Up-right: 6+10 = 16 ✘
So only connected to 7-5 = 2
So path:
7-5 = 2 → right to 8-3 = 5 → right to 9-5 = 4 → down to 9-8 = 1
But still not reaching Moon.
Perhaps the Moon is reached by any yellow tile on the far right.
Look at the far right column:
- 10-2 = 8 ✔
- 10-5 = 5 ✔
- 10+3 = 13 ✘
- 6+7 = 13 ✘
- 10-5 = 5 ✔
- 8+9 = 17 ✘
- 6+10 = 16 ✘
So only 10-2 = 8, 10-5 = 5, and 10-5 = 5 (again) are valid.
So if we can reach 10-2 = 8, we’re done.
How?
From 7-5 = 2 → right to 10-2 = 8
And 7-5 = 2 is connected to 6-5 = 1 → connected to 9-4 = 5 → connected to 8-1 = 7 → connected to 7+2 = 9 → connected to 8+2 = 10 → on the left.
So full path:
1. 8+2 = 10 (start)
2. → 7+3 = 10
3. → 6-1 = 5
4. → 5-2 = 3
5. → 7-5 = 2
6. → 10-2 = 8 (end)
But wait — are 7+3 = 10 and 6-1 = 5 adjacent?
Yes.
6-1 = 5 and 5-2 = 3 — are they adjacent?
Yes, in the grid, 6-1 = 5 is above 5-2 = 3.
Then 5-2 = 3 and 7-5 = 2 — are they adjacent?
Yes, diagonally.
Then 7-5 = 2 and 10-2 = 8 — are they adjacent?
Yes, horizontally.
So the path is:
8+2 = 10
↓
7+3 = 10
↓
6-1 = 5
↓
5-2 = 3
↓
7-5 = 2
→
10-2 = 8
And 10-2 = 8 is on the right edge, near the Moon.
✔ This is a valid path!
Now verify all steps are yellow and result ≤ 10:
- 8+2 = 10 ✔
- 7+3 = 10 ✔
- 6-1 = 5 ✔
- 5-2 = 3 ✔
- 7-5 = 2 ✔
- 10-2 = 8 ✔
All are yellow and results ≤ 10.
Yes, a path exists from Earth to the Moon.
One possible path is:
> 8+2 → 7+3 → 6-1 → 5-2 → 7-5 → 10-2
Each step moves to an adjacent yellow hexagon with a result ≤ 10.
This path goes from the left (Earth) to the right (Moon).
---
- The game involves solving basic arithmetic.
- Only yellow hexagons are usable.
- Only results ≤ 10 are valid (as per "adding and subtracting to 10").
- A valid path exists.
- Answer: The first to solve the path will win the race to the Moon.
🎉 You can win by following the path above!
---
🔍 Understanding the Game
- The board is made of hexagonal tiles, each containing an addition or subtraction problem.
- You start at Earth (on the left) and must reach the Moon (on the right).
- You can only move through hexagons whose answer equals a number on the top row (from 0 to 20).
- But here’s the twist: You're not told which numbers are allowed.
- However, since the title says "Adding and Subtracting to 10", it's likely that only results from 0 to 10 are valid for the path.
But wait — let’s look carefully.
There's a number line at the top:
`0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20`
And yellow hexagons seem to highlight certain problems. But not all yellow ones are necessarily correct — they may just be visual cues.
Wait — actually, in many versions of this game, you can only step on tiles where the result is ≤ 10, or maybe you have to follow a path where each step adds up to a specific total.
But in this version, the goal is to find a continuous path from Earth to the Moon, moving through adjacent hexagons, such that each tile's result is between 0 and 10 inclusive — because the game is "adding and subtracting to 10".
Let’s analyze:
---
✔ Step-by-step Plan
1. Calculate the result of every expression in the hexagons.
2. Only allow movement through hexagons where the result is ≤ 10 (since the title says "to 10").
- But some expressions give results > 10, like:
- `9+4 = 13`
- `10+3 = 13`
- `8+9 = 17`
- `6+10 = 16`
- etc.
- So if we restrict to answers ≤ 10, those are invalid.
But notice: some yellow tiles have answers over 10, so maybe the rule isn't that strict.
Wait — perhaps the yellow tiles are the only ones you can use?
Let’s check that idea.
---
🟡 Yellow Tiles vs. White Tiles
In the image:
- Yellow tiles are highlighted.
- White tiles are not.
So perhaps:
> You can only move on yellow tiles.
Let’s test that.
---
🧮 Calculate All Yellow Tile Results
Let’s go through each yellow hexagon and compute its value:
```
Top row (left to right):
6-1 = 5
9+4 = 13 → ✘ too big? but yellow
7-5 = 2
10-2 = 8
Next row:
8+2 = 10
7+2 = 9
6+5 = 11 → ✘
9-0 = 9
10-5 = 5
Next:
9+3 = 12 → ✘
8-1 = 7
9-4 = 5
6-5 = 1
10+3 = 13 → ✘
Next:
7+0 = 7
3+5 = 8
8+5 = 13 → ✘
3+6 = 9
6+7 = 13 → ✘
Next:
7+3 = 10
6+6 = 12 → ✘
7+7 = 14 → ✘
8-7 = 1
6+7 = 13 → ✘
Next:
6-2 = 4
9-3 = 6
5+4 = 9
3+8 = 11 → ✘
10-5 = 5
Next:
9+4 = 13 → ✘
7-4 = 3
5+6 = 11 → ✘
6+9 = 15 → ✘
9-2 = 7
Next:
6-1 = 5
5-5 = 0
1+8 = 9
7-6 = 1
8+9 = 17 → ✘
Next:
5-2 = 3
6+4 = 10
6+6 = 12 → ✘
9+9 = 18 → ✘
6+10 = 16 → ✘
Next:
5+7 = 12 → ✘
6+8 = 14 → ✘
8-3 = 5
7+8 = 15 → ✘
9-8 = 1
Next:
3-2 = 1
7-5 = 2
9-5 = 4
```
Now, list all yellow tiles with their values:
| Expression | Result |
|-----------|--------|
| 6-1 | 5 |
| 9+4 | 13 |
| 7-5 | 2 |
| 10-2 | 8 |
| 8+2 | 10 |
| 7+2 | 9 |
| 6+5 | 11 |
| 9-0 | 9 |
| 10-5 | 5 |
| 9+3 | 12 |
| 8-1 | 7 |
| 9-4 | 5 |
| 6-5 | 1 |
| 10+3 | 13 |
| 7+0 | 7 |
| 3+5 | 8 |
| 8+5 | 13 |
| 3+6 | 9 |
| 6+7 | 13 |
| 7+3 | 10 |
| 6+6 | 12 |
| 7+7 | 14 |
| 8-7 | 1 |
| 6+7 | 13 |
| 6-2 | 4 |
| 9-3 | 6 |
| 5+4 | 9 |
| 3+8 | 11 |
| 10-5 | 5 |
| 9+4 | 13 |
| 7-4 | 3 |
| 5+6 | 11 |
| 6+9 | 15 |
| 9-2 | 7 |
| 6-1 | 5 |
| 5-5 | 0 |
| 1+8 | 9 |
| 7-6 | 1 |
| 8+9 | 17 |
| 5-2 | 3 |
| 6+4 | 10 |
| 6+6 | 12 |
| 9+9 | 18 |
| 6+10 | 16 |
| 5+7 | 12 |
| 6+8 | 14 |
| 8-3 | 5 |
| 7+8 | 15 |
| 9-8 | 1 |
| 3-2 | 1 |
| 7-5 | 2 |
| 9-5 | 4 |
Now, filter out any yellow tile with result > 10 (since the game is "to 10"):
Valid yellow tiles (result ≤ 10):
| Expression | Result |
|----------|--------|
| 6-1 | 5 |
| 7-5 | 2 |
| 10-2 | 8 |
| 8+2 | 10 |
| 7+2 | 9 |
| 9-0 | 9 |
| 10-5 | 5 |
| 8-1 | 7 |
| 9-4 | 5 |
| 6-5 | 1 |
| 7+0 | 7 |
| 3+5 | 8 |
| 3+6 | 9 |
| 7+3 | 10 |
| 6-2 | 4 |
| 9-3 | 6 |
| 5+4 | 9 |
| 10-5 | 5 |
| 7-4 | 3 |
| 9-2 | 7 |
| 6-1 | 5 |
| 5-5 | 0 |
| 1+8 | 9 |
| 7-6 | 1 |
| 5-2 | 3 |
| 6+4 | 10 |
| 8-3 | 5 |
| 9-8 | 1 |
| 3-2 | 1 |
| 7-5 | 2 |
| 9-5 | 4 |
We now need to find a continuous path from Earth (left side) to Moon (right side) using only these yellow tiles with answers ≤ 10.
Let’s try to trace a possible path.
---
🚀 Tracing the Path
Start near Earth (left edge).
Look at the first column (leftmost):
- 8+2 = 10 ✔ (yellow)
- 2-2 = 0 ✘ (white) → skip
- 7+3 = 10 ✔
- 9+4 = 13 ✘ (too big)
- 6-1 = 5 ✔
- 5+7 = 12 ✘
- 3-2 = 1 ✔
So valid yellow tiles on the left:
- 8+2 = 10 (top-left)
- 7+3 = 10
- 6-1 = 5
- 3-2 = 1
Now, from 8+2 = 10, neighbors:
- Right: 9+3 = 12 ✘ (invalid)
- Down-right: 9+3 = 12 ✘
- Down: 7+3 = 10 ✔
- Down-left: 2-2 = 0 ✘
So from 8+2 → down to 7+3 = 10 ✔
From 7+3 → neighbors:
- Right: 6-2 = 4 ✔
- Down-right: 9+4 = 13 ✘
- Down: 6-1 = 5 ✔
- Down-left: 7+0 = 7 ✔
So multiple options.
Let’s try:
Path attempt:
1. 8+2 = 10 (start)
2. ↓ to 7+3 = 10
3. ↓ to 6-1 = 5
4. → to 5-5 = 0? Wait, 5-5 is white, but 5-5 is not yellow → cannot use.
Wait — 5-5 is white, so even though result is 0, it's not yellow → invalid.
But 6-1 = 5 is yellow, and its neighbors:
- Up: 7+3 = 10 ✔
- Right: 7+4 = 11 ✘ (white)
- Down: 5-2 = 3 ✔ (yellow!)
- Down-left: 5+7 = 12 ✘
So from 6-1 = 5 → down to 5-2 = 3
Then from 5-2 = 3 → neighbors:
- Right: 6+8 = 14 ✘
- Down: 6+9 = 15 ✘
- Down-right: 7-5 = 2 ✔ (yellow)
So → 7-5 = 2
Then from 7-5 = 2 → right to 8-3 = 5 ✔
→ 8-3 = 5
Then → right to 9-5 = 4 ✔
→ 9-5 = 4
Then → right to 7+8 = 15 ✘
Or down? No.
Wait — 9-5 = 4 has neighbor:
- Up-right: 6+4 = 10 ✔
But 6+4 = 10 is above it.
Wait — let’s map positions better.
Instead, let’s try another route.
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Let’s consider a central path.
Start from 8+2 = 10 → down to 7+3 = 10
→ down to 6-1 = 5
→ down to 5-2 = 3
→ down to 7-5 = 2
→ right to 8-3 = 5
→ right to 9-5 = 4
→ right to 7+8 = 15 ✘
No.
Wait — 8-3 = 5 has other neighbors?
- Up: 6+8 = 14 ✘
- Up-right: 6+4 = 10 ✔
Yes! 6+4 = 10 is yellow and adjacent.
So from 8-3 = 5 → up-right to 6+4 = 10
Then from 6+4 = 10 → up to 5+6 = 11 ✘
→ right to 6+6 = 12 ✘
→ down to 8-3 = 5 already visited
→ down-right: 7+8 = 15 ✘
→ up-left: 5-5 = 0 ✘ (white)
Not helpful.
Alternative path:
Try starting from 3-2 = 1 (bottom-left)
→ up to 6-1 = 5 ✔
→ up to 7+3 = 10 ✔
→ up to 8+2 = 10 ✔
Then → right to 9+3 = 12 ✘
→ down to 7+0 = 7 ✔
→ down to 6+6 = 12 ✘
→ right to 8-1 = 7 ✔
→ right to 9-4 = 5 ✔
→ right to 8+5 = 13 ✘
→ down to 7+7 = 14 ✘
→ down-right: 8-7 = 1 ✔
→ right to 3+6 = 9 ✔
→ right to 6+7 = 13 ✘
→ down to 9-2 = 7 ✔
→ right to 10-5 = 5 ✔
→ right to 10-5 = 5 again? Wait.
Wait — 10-5 = 5 appears twice.
One is at top-right, one is lower.
Let’s look at 10-5 = 5 (lower right):
It is adjacent to 9-2 = 7, and then to 8+9 = 17 ✘
But 10-5 = 5 is yellow, and its neighbors:
- Left: 9-2 = 7 ✔
- Up: 3+8 = 11 ✘
- Down: 8+9 = 17 ✘
- Down-right: 6+10 = 16 ✘
So no way to go further.
But earlier we had 9-4 = 5, then 8-7 = 1, then 3+6 = 9, then 9-2 = 7, then 10-5 = 5
Can we go from 10-5 = 5 to 10-2 = 8? Are they adjacent?
Let’s check layout.
Looking at the grid:
Top row:
- 6-1 (5), 9+4 (13), 7-5 (2), 10-2 (8)
Then below:
- 8+2 (10), 7+2 (9), 6+5 (11), 9-0 (9), 10-5 (5)
So 10-2 = 8 is at top-right, 10-5 = 5 is below it.
Are they adjacent? Yes — vertically.
So 10-2 = 8 → down to 10-5 = 5
Then from 10-5 = 5 → down to 10+3 = 13 ✘
→ left to 9-0 = 9 ✔
→ left to 6+5 = 11 ✘
→ down to 6-5 = 1 ✔
→ down to 10+3 = 13 ✘
→ down to 6+7 = 13 ✘
Not working.
Wait — what about 9-0 = 9?
It's yellow, result 9.
Neighbors:
- Up: 7-5 = 2 ✔
- Down: 9-4 = 5 ✔
- Left: 6+5 = 11 ✘
- Right: 10-5 = 5 ✔
So yes, 9-0 = 9 is connected.
But how to get from left to right?
Let’s try this path:
Start at 8+2 = 10 (left-top)
→ down to 7+3 = 10
→ down to 6-1 = 5
→ down to 5-2 = 3
→ down to 7-5 = 2
→ right to 8-3 = 5
→ up-right to 6+4 = 10
→ right to 7+8 = 15 ✘
No.
Wait — 8-3 = 5 → right to 9-5 = 4 ✔
→ right to 7+8 = 15 ✘
→ up to 6+8 = 14 ✘
→ down to 6+9 = 15 ✘
Dead end.
Alternative: from 9-4 = 5 → right to 8+5 = 13 ✘
→ down to 8-7 = 1 ✔
→ right to 3+6 = 9 ✔
→ right to 6+7 = 13 ✘
→ down to 9-2 = 7 ✔
→ right to 10-5 = 5 ✔
→ right to 8+9 = 17 ✘
→ down to 6+10 = 16 ✘
Still stuck.
But 10-5 = 5 is near the Moon.
Is there a way to reach 10-2 = 8?
Yes — from 9-0 = 9 → up to 7-5 = 2 → up to 9+4 = 13 ✘
No.
Wait — 10-2 = 8 is at top-right.
Its neighbors:
- Left: 7-5 = 2 ✔
- Down: 10-5 = 5 ✔
- Down-left: 9-0 = 9 ✔
So from 10-2 = 8, we can go to 10-5 = 5 or 9-0 = 9
But to get to 10-2 = 8, we need to come from left.
Can we reach 7-5 = 2 from the center?
Yes — 7-5 = 2 is yellow.
Its neighbors:
- Up: 9+4 = 13 ✘
- Down: 6-5 = 1 ✔
- Left: 6+5 = 11 ✘
- Right: 10-2 = 8 ✔
So only way to enter 7-5 = 2 is from 6-5 = 1
And 6-5 = 1 is yellow.
Its neighbors:
- Up: 4+7 = 11 ✘
- Down: 6-5 = 1 → same
- Left: 9-4 = 5 ✔
- Right: 6-5 = 1 → same
- Down-left: 6-5 = 1 → no
Wait — 6-5 = 1 is surrounded by:
- Up: 4+7 = 11 ✘
- Down: 6-5 = 1 → same tile
- Left: 9-4 = 5 ✔
- Right: 6-5 = 1 → same
- Up-left: 6+5 = 11 ✘
- Down-right: 6-5 = 1 → same
So only connection is to 9-4 = 5
So path:
9-4 = 5 → right to 6-5 = 1 → up to 7-5 = 2 → right to 10-2 = 8
Then from 10-2 = 8 → down to 10-5 = 5 → down to 10+3 = 13 ✘
But 10-5 = 5 is also connected to 9-0 = 9 → left to 6+5 = 11 ✘
No way to continue.
But wait — 10-5 = 5 is also connected to 9-0 = 9, which is connected to 9-4 = 5, which is connected to 8-1 = 7, which is connected to 7+2 = 9, which is connected to 8+2 = 10, which is on the left.
So we can make a loop, but not a clear path from left to right.
Perhaps the intended path is to go through the center.
Let’s try:
Start: 8+2 = 10 → down to 7+3 = 10 → down to 6-1 = 5 → down to 5-2 = 3 → down to 7-5 = 2 → right to 8-3 = 5 → right to 9-5 = 4 → right to 7+8 = 15 ✘
No.
Another idea: 6+4 = 10 is yellow.
Its neighbors:
- Up: 5+6 = 11 ✘
- Down: 8-3 = 5 ✔
- Left: 5-5 = 0 ✘
- Right: 6+6 = 12 ✘
- Up-right: 6+8 = 14 ✘
- Down-right: 7+8 = 15 ✘
Only connected to 8-3 = 5
Which is connected to 7-5 = 2, etc.
Still no.
Wait — what about 3-2 = 1 → up to 6-1 = 5 → up to 7+3 = 10 → up to 8+2 = 10 → right to 9+3 = 12 ✘
No.
Perhaps the only viable path is through the middle row.
Let’s try:
Start at 8+2 = 10 → down to 7+3 = 10 → down to 6-1 = 5 → down to 5-2 = 3 → down to 7-5 = 2 → right to 8-3 = 5 → up-right to 6+4 = 10 → right to 7+8 = 15 ✘
No.
Alternatively, from 8-3 = 5 → down to 6+9 = 15 ✘
All dead ends.
But wait — 9-5 = 4 → down to 9-8 = 1 ✔
→ right to 9-8 = 1 → down to 9-8 = 1 → no
9-8 = 1 is at bottom-right.
Its neighbors:
- Left: 7-5 = 2 ✔
- Up: 7+8 = 15 ✘
- Up-right: 6+10 = 16 ✘
So only connected to 7-5 = 2
So path:
7-5 = 2 → right to 8-3 = 5 → right to 9-5 = 4 → down to 9-8 = 1
But still not reaching Moon.
Perhaps the Moon is reached by any yellow tile on the far right.
Look at the far right column:
- 10-2 = 8 ✔
- 10-5 = 5 ✔
- 10+3 = 13 ✘
- 6+7 = 13 ✘
- 10-5 = 5 ✔
- 8+9 = 17 ✘
- 6+10 = 16 ✘
So only 10-2 = 8, 10-5 = 5, and 10-5 = 5 (again) are valid.
So if we can reach 10-2 = 8, we’re done.
How?
From 7-5 = 2 → right to 10-2 = 8
And 7-5 = 2 is connected to 6-5 = 1 → connected to 9-4 = 5 → connected to 8-1 = 7 → connected to 7+2 = 9 → connected to 8+2 = 10 → on the left.
So full path:
1. 8+2 = 10 (start)
2. → 7+3 = 10
3. → 6-1 = 5
4. → 5-2 = 3
5. → 7-5 = 2
6. → 10-2 = 8 (end)
But wait — are 7+3 = 10 and 6-1 = 5 adjacent?
Yes.
6-1 = 5 and 5-2 = 3 — are they adjacent?
Yes, in the grid, 6-1 = 5 is above 5-2 = 3.
Then 5-2 = 3 and 7-5 = 2 — are they adjacent?
Yes, diagonally.
Then 7-5 = 2 and 10-2 = 8 — are they adjacent?
Yes, horizontally.
So the path is:
8+2 = 10
↓
7+3 = 10
↓
6-1 = 5
↓
5-2 = 3
↓
7-5 = 2
→
10-2 = 8
And 10-2 = 8 is on the right edge, near the Moon.
✔ This is a valid path!
Now verify all steps are yellow and result ≤ 10:
- 8+2 = 10 ✔
- 7+3 = 10 ✔
- 6-1 = 5 ✔
- 5-2 = 3 ✔
- 7-5 = 2 ✔
- 10-2 = 8 ✔
All are yellow and results ≤ 10.
✔ Final Answer:
Yes, a path exists from Earth to the Moon.
One possible path is:
> 8+2 → 7+3 → 6-1 → 5-2 → 7-5 → 10-2
Each step moves to an adjacent yellow hexagon with a result ≤ 10.
This path goes from the left (Earth) to the right (Moon).
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📝 Summary
- The game involves solving basic arithmetic.
- Only yellow hexagons are usable.
- Only results ≤ 10 are valid (as per "adding and subtracting to 10").
- A valid path exists.
- Answer: The first to solve the path will win the race to the Moon.
🎉 You can win by following the path above!
Parent Tip: Review the logic above to help your child master the concept of printable math board games for first grade.