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Summing consecutive numbers

11 to 14

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

problem

Favourite

Connect three

11 to 16

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

problem

Favourite

A4 fraction addition

7 to 11

Try adding fractions using A4 paper.

problem

Seven square numbers

7 to 11

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

problem

Next number

7 to 11

Find the next number in this pattern: 3, 7, 19, 55 ...

problem

Chord

16 to 18

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

problem

Inspector Morse

11 to 14

You may like to read the article on Morse code before attempting this question. Morse's letter analysis was done over 150 years ago, so might there be a better allocation of symbols today?