# GeekDad Puzzle of the Week: Sam’s Sly Shipping Service – Solution

Photo: Sillof's Gaslight Justice League

This week, super-villain Jack Smith’s right-hand, Samantha Sly is shipping out counterfeit action figures to a number of duped toy stores around the US; she needed a little help with packing the shipping cartons. Thanks to Kenny Taylor, Sam found a way to satisfy her customers and her boss, which is usually impossible. Kenny will receive a \$50 gift code from ThinkGeek! The rest of you may find a code for \$10 off a \$40 purchase at the end of this post.

Come back on Monday for next week’s puzzle.

Continue reading for the puzzle and solution.

### Puzzle

Samantha Sly, known by those who like pain as Side-Kick Sam, is tasked with shipping counterfeit action figures to a number of stores who think they are receiving the real deal.

This is what we know:
Side-Kick Sam has to have the figures shipped to toy stores in the following states. To protect the stores’ identities, we’ll just show the number of stores in each state.
Utah: three stores
Arizona: five stores
California: seven stores

To avoid suspicion and to handle unexpected problems, once on the road every truck must be able to be redirected to any of the states at the last moment, without any store receiving less than what they expected.

What is the minimum number of action figures Sam should have loaded onto each truck to guarantee that the deliveries go smoothly?

### Solution

The degenerate answer is 0. That minimizes the number of orders in each truck, but it guarantees that no stores will receive delivery. Obviously this isn’t the answer I’m looking for.

A single case on a single truck won’t work either because we would only be able to deliver to a single store and the other stores will receive nothing. Similarly for 3, 4, 5, and 7. What about 11?

If Sam loaded a single truck with 11 orders she would not be able to deliver to Nevada and another state if something went wrong. What if Sam loaded five trucks, each with 11 cases? This would solve the problem as long as she only needed to redirect one or two trucks (to Utah and Colorado). If three trucks were pulled over or otherwise lost, all states could not be served.

Finally, Kenny’s answer is that Sam should load up the sum of all stores (30) in each truck. This would allow any one truck to deliver to all states. How many trucks would she need? If everything went well: one. The puzzle states that we cannot assume everything will go well. Will two trucks do it? Yes, if only one is lost. Sam would be best served by sending five trucks, each loaded with 30 orders.

I accepted several other solutions (with accompanying logic) as well and threw their owners’ names into the hat. Congratulations to Kenny, whose name was pulled from the hat.

Your code for \$10 off purchases of at least \$40 at Thinkgeek is puzzling.