Determine all possible values of a 5-digit positive integer N, such that:
- The first two digits of N, read as a two digit number, are three times the third digit, and:
- The last two digits of N (read as a two digit number) are twice the third digit, and:
- The sum of all the digits of N is 27.
Prove that there are no others.
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
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Posted by Charlie
on 2014-04-22 13:28:47 |
Proof
