HINT 2: The sum of the three digits must be divisible by both 9 and by 2. The only
possible sums of three digits that are divisible by 9 are 9, 18, and 27 (27 is the highest possible total
of three digits where all three are 9's). If the sum is 9 or 27, the number it is not divisible by two so
we know the sum of the digits is 18.
ANSWER:
10.
EXPLANATION: Since the number is divisible by 9, we know the sum of the digits is
divisible by 9, so the digits add up to 9, 18, or 27 (27 is the highest possible total of three digits
where all three are 9's). Since the number contain even digits only, we know the sum of the digits must
be divisble by 2 which means the sum of the three digits is 18. The only combinations of three even
digits that add up to 18 are:
2, 8, 8
4, 6, 8
6, 6, 6
There are 10 numbers that have these combinations of digits arranged in different ways:
2, 8, 8: 288, 828, 882,
4, 6, 8: 468, 486, 648, 684, 846, 864,
6, 6, 6: 666.
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
