[bonanova]

fat x fat = nonfat

[curr3nt]

376 * 376 = 141376

[Guest]

625

[Guest]

-1 X -1 = 1

-1 = fat

1 = nonfat

[Guest]

I also got 376*376=141,376. I did it by trial and error, guessing that the last number was 6. But is there an algorithm for this?

BTW, 625*625=390,625 which does not work for "non"

[Guest]

I also got 376*376=141,376. I did it by trial and error, guessing that the last number was 6. But is there an algorithm for this?

BTW, 625*625=390,625 which does not work for "non"

Oh my bad.

I did not account for the n's, only the "fat"s

[Guest]

-1 X -1 = 1

-1 = fat

1 = nonfat

Given that the op did not mention what to do and most people (including me) blindly went into the alphametics, I thought this "out of the box answer" deserved a special mention! Good one, that's not confusing!

I also got 376*376=141,376. I did it by trial and error, guessing that the last number was 6. But is there an algorithm for this?

For the non-out-of-the-box thinkers like me

FAT x FAT = NONFAT

T can be 0,1,5 or6

0 can be ruled out for T because nonfat contains only one T (0).

Out of 1, 5 and 6, for AT, there are 3 possibilities: 01, 25, 76

For AT as 01,

F01 x F01 = (100F + 1)² = 10⁴F² + 200F + 1

F must be greater than 3 in order to have 6 digits in the product. Since 2F must end in F, there is only only possibility for F which is 0. So, 01 can be ruled out for AT

For AT as 25,

25x25 = 625

F25 x F25 = (100F + 25)² = 104F² + 5000F + 25²

So, all F25 would end in 625; which means the only possibility for FAT is 625

Since 625 x 625 does not give NON625, this can also be ruled out

so, AT must be 76

F76 x F76 = 10⁴F² + 2*76*F*100 + 76²

For last 3 digits we only need to see: 76² + 152F*100 i.e. 5776 + (152F)*100 must give F as the third digit

This means that 7 + 2F must give F

This is possible only when F = 3

So, the number must be 376