Posted by **SkaterGirl** on Sunday, December 5, 2010 at 10:34am.

There are three distinct ways to add four positive odd numbers to obtain 10:

1 + 1 + 3 + 5 = 10

1 + 1 + 1 + 7 = 10

1 + 3 + 3 + 3 = 10

Here, distinct means that changing the order of the numbers on the left-hand side of an

equation does not count as a new solution. In how many distinct ways can we add eight odd

positive numbers to obtain 20? Justify your response. Hint: be systematic in your approach!

Problem 2

Find, with justi cation, the smallest integer whose rst digit is 1 and which has the property

that if this digit is transferred to the end of the number, then the number is tripled.