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Locker Unlock (Posted on 2013-07-23) Difficulty: 3 of 5
Al had forgotten his locker combination and was going to be late for class.

But he was able to remember the following things:

  1. Each of the three numbers of the combination can be anywhere between 1 and 39 inclusive.
  2. Each one was different and the sum of the first two numbers was 42. The last two numbers differed by only two, and all three numbers were primes.
His friend remembered the combination and told him, "If you take the three numbers of your combination and multiply them together, the last digit of the product will be ....", and then whispered something in his ear.

With that, Al was able to deduce his combination and open his locker.

What was his combination?

See The Solution Submitted by K Sengupta    
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Solution computer solution | Comment 2 of 4 |

 10   for A=1 to 12
 20   for B=1 to 12
 30   for C=1 to 12
 35       P1=prm(A):P2=prm(B):P3=prm(C):
 40       if P1+P2=42 and abs(P3-P2)=2 then
 50         :if A<>B and B<>C and A<>C then
 60            :Prod=P1*P2*P3
 70            :print using(8,0),P1;P2;P3;Prod
 80   next
 90   next
100   next

shows the possibilities suiting both clues 1 and 2:

                     product
 11      31      29    9889
 13      29      31   11687
 23      19      17    7429
 29      13      11    4147
 31      11      13    4433
 37       5       3     555
 37       5       7    1295

The friend must have whispered "3" into Al's ear, cluing him that his combination was 31, 11, 13.


  Posted by Charlie on 2013-07-23 12:21:01
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