In how many different ways may these nine squares be arranged in three tiers of three so that no square shall have a smaller number than its own below it or to the right of it? The first correct arrangement that will occur to you is I 23 at the top, then 4 5 6 in the second row, and 789 at the bottom, and my sketch gives a second arrangement. How many are there altogether?
Christmas Resources
MathSalamander – a wide variety of maths activities covering most age groups.
Seasonal maths from Resourceaholic, again, has a wide range of activities
TheMathematics Shed has a PDF book with many Christmas puzzles
Solution – The Nine Squares
There are forty-two different arrangements. The positions of the I and 9 are fixed. Always place the 2 beneath the 1. Then, if the 3 be beneath the 2there are five arrangements. If the 3 be to the right of the I there are five arrangements with 4 under the 2, five with 5 under the 2, four with 6 under 2, two with 7 under 2. We have thus twenty-one arrangements in all. But the 2might have been always to the right of I, instead of beneath, and then we get twenty-one reversed and reflected arrangements (practically similar)
Final words (for your Christmas cracker collection)
I noticed my math teacher holding a piece of graph paper yesterday.
I’m guessing she’s plotting something.
What did the circle hear from the triangle?
The triangle said, “You’re pointless.”
What does a mathematician use to plough a field?
They use a pro-tractor.
Happy Christmas
