Do I have to guess?
Hummus’s number has three digits.
One of the digits is a
prime number
,
Another of the digits is a
perfect square
,
and the other digit neither prime nor square.
If the number isn't divisible by 3, then what is the greatest possible value of Hummus’s number?
The answer is 985.
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1 solution
The single digit prime numbers are 2 , 3 , 5 , and 7 . The single digit perfect squares are 0 , 1 , 4 , and 9 , leaving 6 and 8 as neither prime nor perfect square. We'll choose the largest digit in each group and arrange from greatest to least to get the largest possible number, 9 8 7 .But 9 8 7 is divisible by 3 . To get the next greatest number, take the next greatest digit from the group containing 7 .So,the greatest possible value of Hummus’s number is 9 8 5 .