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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
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2 Answers 2

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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.

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    $\begingroup$ 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! $\endgroup$
    – kviiri
    May 30, 2017 at 13:20
  • $\begingroup$ Thanks. I edited the answer with the explanation. See if it is what you expected. $\endgroup$
    – Marius
    May 30, 2017 at 13:28
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    $\begingroup$ @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. $\endgroup$
    – BmyGuest
    May 30, 2017 at 14:15
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Final answer:

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

Explanation:

  • A + E is even: A and E have the same parity
  • B is A cubed: B and A have the same parity
  • D is B divided by 2: B is even

- From these statements, E is even. From the last statement, "E is prime", E must an even prime, so E = 2.
- C is the least among all numbers and is the only odd integer, so to be less than 2 it must be 1.
- A can't be 2 because it is distinct from E, but it can't be larger than 5 because B = A cubed is less than 100, so A is 4.
- This leaves B = A cubed = 64, and D = B divided by 2 = 32.

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