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'Month Mania' printed from http://nrich.maths.org/
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!
BOTTOM LEFT and BOTTOM RIGHT
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 !