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.

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¢.