### Primes and Products

Pete and Dick share a birthday in early November but are six years apart in age.

Dick tells the team: “Pete’s age is now a prime, and my age is now the product of two odd primes.”

Pete adds, “This last happened 12 years ago.”

How old is Dick?

### Two Pints of Cider

Team member Janice recently visited the U.K. and poses this puzzle to her teammates: You have three containers that can hold exactly 15, 10, and 6 pints. The 15-pint container starts full of cider. You want to measure out exactly 2 pints of cider, drink it all, and end with an empty 15-pint container and 8 and 5 pints of cider in the other two containers.

What transfers should you make to accomplish this?

## Solutions to week 113

In Prime Presents 1 there were six gifts with a bill of \$2 + \$3 + \$5 + \$41 + \$67 + \$89 = \$207. In Prime Presents 2 there were six gifts with a bill of \$2 + \$3 + \$5 + \$67 + \$89 + \$401 = \$567.

Prime Presents 1 answer explained: A bill of \$2 + \$3 + \$5 + \$41 + \$67 + \$89 gives a total \$207. To use \$8 we must use \$83 or \$89; to use \$6 we must use \$61 or \$67 and to use \$5 we must use \$5, \$53, or \$59. This requires that one of the gifts was \$5, otherwise, we would get a total greater than \$207. To use \$1, \$4, and \$6, we must use \$41 and \$67 or \$47 and \$61. The best way to use \$2, \$3, \$8, and \$9 is then \$2 + \$3 + \$89. Note that using \$41 + \$67 or \$47 + \$61 gives an ambiguity in what the individual gifts could have cost.