perplexus.info :: Numbers : 1st+2nd=3rd

1st+2nd=3rd (Posted on 2011-09-14)

If we place 192 in the 1st row, 384 in the second row and 576 in the 3rd row, then we get a 3x3 square, exhausting all non-zero digits.
In this square 1st row + 2nd row = 3rd row.

Please provide all other arrangements, satisfying this condition.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Mod 9 analysis

Comment 3 of 3 |

By the way:

The 3rd row must be a multiple of 9.

Proof:

Let a = first row, b = 2nd row, c = 3rd row.

By casting out 9's,

a + b + c = 0 (mod 9) (because all digits are there exactly once)

Also, a + b - c = 0 (initial problem)

Subtracting the two equations, we get

2c = 0 mod 9,

So c = 0 mod 9

Posted by Steve Herman on 2011-09-15 10:00:53

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