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All divisible by 7 (Posted on 2008-11-04) Difficulty: 2 of 5
Imagine a rectangle divided into 3x4 squares, and put a digit in each square.
     +---+---+---+---+
     | a | b | c | d |  A
     +---+---+---+---+
     | e | f | g | h |  B
     +---+---+---+---+
     | i | j | k | l |  C
     +---+---+---+---+
       D   E   F   G
The number abcd is denoted by A, that is, A = 1000a + 100b + 10c + d, and the same for the other 2 horizontal numbers B and C.

The number aei is denoted by D, that is, D = 100a + 10e + i, and the same for the other 3 vertical numbers E, F and G.

Prove that if any 6 of these numbers (A, B, C, D, E, F, G) are divisible by 7, then the last number must also be divisible by 7.

See The Solution Submitted by pcbouhid    
Rating: 3.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Problems with the posted solution - you´re rightpcbouhid2008-11-13 09:58:10
Problems with the posted solutionSteve Herman2008-11-12 23:00:21
re(2): Proof and ExtensionsSteve Herman2008-11-06 14:20:11
re: Proof and ExtensionsCharlie2008-11-06 11:47:26
SolutionProof and ExtensionsSteve Herman2008-11-06 02:26:51
Questionre: proof not understoodCharlie2008-11-04 16:34:49
proofxdog2008-11-04 14:40:41
Solutioncomputer-assisted proofCharlie2008-11-04 13:19:14
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