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Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Month Mania

Age 5 to 11 Challenge Level:

John from St. Edburg's wrote;

I made the numbers into a triangle, starting in the top corner. When I got to the bottom I started again at the top. I noticed that the middle row and the middle column both added up to $75$.
I wondered what would happen if I went down, then up, then down again in a zigzag instead of just filling in the numbers downwards. I had no idea that the middle row and the middle column were going to add up to $75$ again!
I tried putting the numbers in a different order again, starting in the bottom left hand corner. In the bottom left picture I did the same zigzag as in the top right, and in the bottom right picture the numbers are filled in diagonally from top to bottom. I wondered if the middle row and middle column would add up to $75$ again, but they didn't. They all added up to $70$!
When I put the numbers into this grid, I spotted that on diagonal rows the units repeat. This is because each number down the diagonals is $5$ higher than the one before it ($1, 6, 11, 16$ and $13, 18, 23, 28$).

Well done this was really a good investigation for you - keep going !