# Fun with numbers: solve A to E

A, B, C, D and E are five distinct non-negative integers no greater than 99. Can you figure out their values based on the following simple clues?

• Not all of the five numbers have the same parity
• A + E is even
• B is A cubed
• C is the least among the five numbers
• D is B divided by 2
• E is prime

A = 4
B = 64
C = 1
D = 32
E = 2.

Explanation:

D is B divided by 2 means B is even.
This and B is A cubed means A is even.
This and A + E is even means E is even.
This and E is prime means E = 2 since it's the only even prime.
C is the least among the five numbers means C is smaller than 2. So C = 1 or 0.
Coming back to B is a perfect cube of an even number and it's below 100 it means B can be 8 or 64.
For B to be 8 A should be 2, but that's not possible since E = 2.
So B = 64. This gets you A = 4 and D = 32.
A, B, D, E are all even. This means C has to be odd. So C = 1

Recap to see that all of them fit:

$A + E = 4 + 2 = 6$ which is even - checked
B is A cubed => $64 = 4^3$ - checked
$C = 1 < 2 < 4 < 32 < 64$ - checked
D is B divided by 2: $32 = \frac{64}{2}$ - checked
E is prime. 2 is prime - checked.

• Wow, that was fast. I'm posting this here as a P.O.C. of a mystery geocache and it seems I might want to crank up the difficulty gears a bit for a suitable challenge. Excellent work! – kviiri May 30 '17 at 13:20
• Thanks. I edited the answer with the explanation. See if it is what you expected. – Marius May 30 '17 at 13:28
• @kviiri I think people here at PuzzlingSE are a notch above the average geocache searcher. I think the difficutly level you have is nice for your application. – BmyGuest May 30 '17 at 14:15