Problem Solving Set 10

13 July 2012

1. Let f : ℝ → ℝ be a continuous function. Suppose that for any c > 0, the graph of f can be moved to the graph of cf using only a translation or a rotation. Does this imply that f(x) = ax + b for some real numbers a and b?

2. Find a 10-digit number using each of the numbers from 0 to 9 once such that the last i digits are perfectly divisible by i. (For example the 3-digit number 120 has this property: 1 | 0, 2 | 20, 3 | 120.)