Year 7 Being curious

In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

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?