Card sums

Today we did one of the 52 activities in mathemagician Andrew Jeffrey’s great book. Andrew very kindly donated the proceeds of this book to SAMI.

This activity involved shuffling the Aces through to 9s in a pack of cards and setting them out in the following format to gain the biggest total. The first two cards represent a two digit number. We played many games of 1 min each to see who could find the biggest total (without a calculator!) and then enjoyed discussing strategy until we found (we think!) a perfect strategy.

The total for the layout of the cards at the top would be 97×1+17*5=182. Can you do better with those six cards?

Motorway problem

Imagine four towns in a square system with side length 1 mile.

You would like to connect all four towns by motorways, using the least amount of road (not necessarily the most efficient for any one particular town).

Here is one option – it would take 4 miles of road. Can you do better?

Once you have had plenty of time to think and try and find and evaluate the best route, watch this video for the solution.