Find the smallest positive integer that is a multiple of 35 whose digits are all the same.

Since 35 = 7 * 5 the answer must be all 5's. When divided by 5 it's all 1's and divisible by 7 (easier to key into the calculator than 35). 1 and 11 are obviously not divisible by 7, so starting at 111, division of all-1 integers by 7 gives:

15.85714285714286
158.7142857142857
1587.285714285714
15873

That last was of 111111, so the sought answer is 5 times this, or 555555.

Posted by Charlie on 2006-05-03 10:35:15