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Smallest Multiple of 99 (Posted on 2016-07-19) Difficulty: 3 of 5
Determine the minimum positive integer multiple of 99, such that
The sum of the digits is 99, and
The multiple begins and ends with 97.

No Solution Yet Submitted by K Sengupta    
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Solution An analytic approach Comment 3 of 3 |

We are looking for a number 97xxxxxxxxx97 with s.o.d.=99, meaning that the missing digits sum up to 99-32=67  which is  4+7*9,- so the minimal choice would be xy9999999, where x+y=4.

Out of 3 candidates to be tested for divisibility by 99(97229999999,97139999999, 97319999999) the last one fits. **

Answer: 97319999999

**Luckily, the answer came out quickly,- if not,  we should have tried xy8999999, where x+y=5 etc

Edited on July 20, 2016, 11:56 pm
  Posted by Ady TZIDON on 2016-07-20 03:35:26

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