264 This 2x3 grid has an interesting
200 property: 264x200 = 22x60x40.
Build a similar grid using all digits from 2 to 7.
(In reply to
full solution - no programming by pcbouhid)
I know that this problem is almost 8 years old, but it just came up as a random problem, I looked it, and I couldn't let bad math go uncorrected. After all, there could be children reading this.
One of the solvers says:
(CxF) is congruent to (DxExF) (mod 10).
Dividing by F, C is congruent to DxE (mod 10/F).
Since 10/F must be an integer, F is equal to 5 or to 2.
And the rest of the "solution" proceeds from there. The solver only gets away with this because, in this problem, F does happen to equal 2, but that conclusion is unjustified.
Consider 4 x 3 = 2 x 7 x 3 (mod 10). It does not follow that 10/3 is an integer, or that 3 is equal to 5 or 2. In general, any proof that 3 = 5 or 2 is suspect.
re: full solution - no programming
