Question

Prove that given an unlimited supply of 6-cent coins, 10-cent coins, and 15-cent coins, one can make any amount of change larger than 29 cents.

Answer 1

30¢ = 2×15¢

31¢ = 15¢ +10¢ +6¢

32¢ = 2×10¢ +2×6¢

33¢ = 15¢ +3×6¢

34¢ = 10¢ +4×6¢

35¢ = 15¢ +2×10¢

From this 6¢ range, any subsequent values can be reached by adding multiples of 6¢ to these numbers. For example, 36¢ = 2×15¢ +6¢.