Can you solve the following cryptarithm? SEVEN / NINTHS = 7/9

As Rajal said, if you find a number k such that 7k=SEVEN and 9K=NINTHS, you will have solved the problem.

SEVEN can be as low as 10203, or as high as 98786, so k must be between 10203/7 and 98786/7, or 1457 and 14112. Similarly, NINTHS is between 101234 and 989765, so k must also be between 101234/9 and 987965/9, or 11248 and 109973.

Given both conditions, k must be between 11248 and 14112. Thus, SEVEN is between 78736 and 98784, and NINTHS is between 101232 and 127008; this last result allows us to say that N=1, and I=0 or 2.

If NIN=101, then SEVEN must be between 78737 and 79323, so E=8 or 9. If E=8, SEVEN=78V81; as it must be greater than 78737, then V=9; SEVEN=78981, so NINTHS=101547: a solution!

To finish this case, we should study E=9, and then go on to NIN=121... but IF there is only one solution, why bother? ;-)

Edited on September 27, 2004, 2:54 pm

Posted by e.g. on 2004-09-27 14:47:09