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2-digit numbers by clue

For each set of clues, name the only 2-digit number satisfying those clues.
A 2-digit number is defined to be an integer between 10 and 99 (01 doesn't count, for instance).
Quiz by
TWM03
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Last updated: August 6, 2017
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First submittedAugust 5, 2017
Times taken39
Average score53.3%
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Clue(s)
Answer
Square, digits add to 10.
64
Prime, both digits are themselves prime, the first digit is at least three more than the last.
73
This number, and this number turned upside-down, which is smaller, have a 2-digit highest common factor.
99
Prime, digits differ by one, if you subtract 2 it is still prime.
43
Divisible by 9, if you divide by 3 it is still divisible by 9, smaller than 39.
27
A prime factor of 999
37
A perfect number
28
Differs by one from a square, differs by one from a cube not equal to the square.
26
Clue(s)
Answer
Digits add to 12, when divided by 4 the answer is divisible by 4.
48
Digits add to 9, not a square or cube, first digit is prime, not divisible by 4
54
3 distinct prime factors, smaller than 37.
30
Only one distinct prime factor, greater than 71, not prime.
81
A factorial
24
Square, if you add each digit and the product of the digits, you get the number itself.
49
Its square root is between 3 and 4, Digits add to more than 5.
15
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2 Comments
marathon16
+1
Level 49
Aug 6, 2017
Excellent quiz. However, the 5th question has another answer, 2x the one given. Perhaps you should specify that if more than 2 numbers fit the criteria, the smallest one is the one you want.
TWM03
+1
Level 72
Aug 6, 2017
OK, I have changed it now so that there is only one answer. I had intended for there only to be one answer to each question. I have checked the rest and I think that is the only mistake. Please tell me if there are any more.
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