Year 7 Being curious

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

If you move the tiles around, can you make squares with different coloured edges?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?