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5 Digit Number III (Posted on 2014-04-22) Difficulty: 1 of 5
Determine all possible values of a 5-digit positive integer N, such that:
  1. The first two digits of N, read as a two digit number, are three times the third digit, and:
  2. The last two digits of N (read as a two digit number) are twice the third digit, and:
  3. The sum of all the digits of N is 27.
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Solution Proof | Comment 2 of 3 |

Exhaust the center-digit possibilities:

00000 isn't a 5-digit number and doesn't add to 27
03102 has leading zero and adds to 6
06204 similar problems
09306 also
12408 adds to 15
15510 adds to 12
18612 adds to 18
21714 adds to 15
24816 adds to 21
27918 adds to 27  solution




  Posted by Charlie on 2014-04-22 13:28:47
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