All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 All divisible by 7 (Posted on 2008-11-04)
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)

 Subject Author Date re: Problems with the posted solution - you´re right pcbouhid 2008-11-13 09:58:10 Problems with the posted solution Steve Herman 2008-11-12 23:00:21 re(2): Proof and Extensions Steve Herman 2008-11-06 14:20:11 re: Proof and Extensions Charlie 2008-11-06 11:47:26 Proof and Extensions Steve Herman 2008-11-06 02:26:51 re: proof not understood Charlie 2008-11-04 16:34:49 proof xdog 2008-11-04 14:40:41 computer-assisted proof Charlie 2008-11-04 13:19:14

 Search: Search body:
Forums (0)