Smashing time

Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Yesterday, Granny had 12 cups and 10 matching saucers, but this morning she dropped a tray holding one third of the cups and half the saucers, breaking all of those on the tray.

How many of her cups are now without saucers if...

a) all of the cups are identical, and all of the saucers are identical?

b) the cups are all different to each other, and 10 of the cups matched a specific saucer?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.