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What happens if this pdf is the arc of a circle?

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

Can you reproduce the Yin Yang symbol using a pair of compasses?

A challenging activity focusing on finding all possible ways of stacking rods.

Can you place the numbers from 1 to 10 in the grid?

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5×5 array?