Abe challenges Bee to determine a
3digit positive integer N.
It is known that the
number formed by the last two digits of N when divided by 9, yields a remainder of 3.
Abe makes the following statements, precisely one of which is false:
 N divided separately by each of 2, 4, 6, and 8 yields a remainder of 1.
 N divided separately by each of 5 and 7 yields a remainder of 2.
 N divided separately by each of 5 and 11 yields a remainder of 3.
Determine the value of N from the above statements and given clues.
The first clue yields a set of 90 numbers  half even, half odd. Looking at the clues, there is a conflict between clues 2 and three (i.e. division by 5 leaves different remainders), so the false statement must be one of these.
From clue 1, all even number can be eliminated. Dividing the odd ones by both 6 and 8 reduces the set to these five numbers:
121, 193, 457, 721, 793
After dividing these numbers by 5, 7, and 11, the only one with matching remainders is 457.

Posted by hoodat
on 20160628 05:15:07 