Zargon Glasses
Zumf makes spectacles for the residents of the planet Zargon, who have either three eyes or four eyes. So Zumf makes glasses with three lenses and glasses with four lenses.
One day he took orders from nine families. Each family ordered eight glasses, but each order was different.
How many lenses will Zumf need to make all nine orders?
What is the greatest number of lenses a family could need?
How do you know you haven't got that combination already?
It might be helpful to have some counters with either three or four dots on them to represent the eyes.
Here's a solution from Matthew (Nimbin Central School, Australia). He found that 252 lenses would be needed to make all the glasses. He explained how he did it by first working out all the combinations of glasses that made up the 9 orders:
"I wrote down in a grid that was eight wide and nine down, 3 or 4 and we had to be careful not to get the same number of threes or fours as another group of eight. And at the end we found out that there were 36 fours and 36 threes, and when we added all of the numbers together it equalled 252".
Is there another way to do the maths in this problem?