Puzzle 1: The coins of the country of Kakania are available in just three denominations, which are, in increasing order, the krik, the krak, and the krok. It is possible to choose exactly three Kakanian coins to form the sums of 20, 23 and 29. What are the denominations of the Kakanian krik, krak, and krok coins?
(This puzzle came from the 2005 US Puzzle Championship.)
Puzzle 2: The coins of the country of Arcadie are available in just three denominations, namely, 6, 9 and 20. There are several sums that cannot be formed, no matter how many coins are used. One of them is 37. Can you name a higher sum that cannot be formed? Is there a highest impossible sum, or is there an endless sequence of them? (This puzzle appeared on "Car Talk".)
I give up, show me the solution.