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# Number Tiles

## Question

Guest

Something I came across.

Arrange the tiles into a 5x5 grid where the numbers match horizontally and vertically.

Edit for clairification, but possible spoiler hint:

By matching I mean that the vertical and horizontal numbers will match. For example,

if you take the vertical 543 and add the 28 under it to start the grid, you would need the top row to read 54328 also. So:

54328

46

37

2

8

## 2 answers to this question

• 0
bonanova    76

Anti-spoiler: you mean: the grid is symmetric about its [upper left - lower right] diagonal?

If so, no need to peek at the spoiler above...

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bonanova    76

5 4 3 2 8 - can't show the tile boundaries easily, but it should be obvious.

4 6 7 1 9

3 7 0 4 2

2 1 4 1 6

8 9 2 6 7

Here's how:

If a number appears an odd number of times, it has to be on the diagonal.

Five numbers do that: 0[1], 1[3], 5[1], 6[3], 7[3]

Upper left UL corner has to be top or left number on a tile.

Five possibilities: 1[on 3 tiles] 5[on 1 tile] 7[on 1 tile]

Lower right LR corner has to be bottom or right number on a tile.

Three possibilities: 6[on 1 tile] 7[on 2 tiles]

Start eliminating the possibilities. In the order mentioned above,

[1] 1-6 tile.

Requires a 6 beneath the 1.

No 6 appears on the top or left of a tile. Impossible.

[2] 1-9 tile. Requires a 9 to right of the 1.

No 9 appears on top or left of a tile. Impossible.

[3] 1-4 tile.

Requires a 4 to right of the 1. Place the 4-6-7 tile there.

That puts a 6 on the diagonal. OK.

Also requires a 7 right of the 6. Place the 7-0-4 tile there.

That puts a 0 on the diagonal. OK.

Bottom right number must now be 5 or 7. No 5 on bottom or right of a tile, so place 2-6-7 tile there.

Requires a 5 above the 6.

No 5 appears on bottom or left of a tile. Impossible.

[4] 5-4-3 tile.

Requires a 4 right of the 5. Place the 4-6-7 tile there.

That creates the diagonal-6. Now the only possible BR number is 7. Place the 2-6-7 tile there.

That requires a 6 above the 7. Place the 1-6 tile there.

A 2 must be above the 6. Place the 2-9 tile there.

A 9 must be left of the bottom-row 2. Place the 1-9 tile there.

The remaining diagonal number is 0. Place the 7-0-4 tile there.

4 must be right of the 0. Place the 1-4 tile there.

Finally place the 2-8 tile and the 3-2-8 tile in their slots.

Check for symmetry.

Done.

[5] 7-0-4-tile.

Requires a 0 right of the 7.

No 0 appears on top or left of a tile. Impossible.

[6] 1-6 tile.

Requires a 1 above the 6.

No 1 appears on bottom or right of a tile. Impossible.

[7] 4-6-7 tile.

Requires a 6 to left of 7. Place the 1-6 tile there.

That places a 1 where a 4 has to be. Impossible.

[8] 2-6-7 tile.

Hmm... looks exactly like [4] above. It is. Done.

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