Puzzles by Paul Godding

Paul’s Puzzles

By Paul Godding

The Main Challenge

Using the numbers 2, 4 and 6 once each, together with + – × ÷, find the SIX target numbers from the following list that are mathematically possible to make: 12 14 16 18 20 22 24 26 28 30 The Mathematically Possible Challenge Using 8, 9 and 10 once each, with + –The 7puzzle Challenge × ÷ available, which is the ONLY number it is possible to make from the list below?

The playing board of the 7puzzle game is a 7by-7 grid of 49 different numbers, ranging from 2 up to 84. The 2nd & 6th rows contain the following fourteen numbers: 4 8 12 16 20 24 28 32 36 40

#4TimesTable

5 8 12 17 18 20 28 33 48 49 55 56 63 64

What is the sum of the cube numbers?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1). There are THREE ways of making 43 when using Lagrange’s Theorem.

Can you find them?

The Target Challenge

Can you arrive at 43 by inserting 4, 5, 8 and 9 into the gaps on each line?

• ◯×◯–◯÷◯ = 43 • ◯²+◯×(◯–◯) = 43 • (◯+◯)×◯–◯² = 43 • (◯×√◯×√◯)–◯ = 43 • (◯–√◯)×◯+◯ = 43

Solutions: http://7puzzleblog.com/answers/

Hello, my name is Paul Godding. I am a full-time professional private maths tutor based in the south-east of Wales who delivers face-to-face tuition locally as well as online tuition to students globally. It would be lovely to hear from you, so feel free to click paul@7puzzle.com if you wish to secure maths tuition for you or your child. Alternatively, you can ring/message/WhatsApp me from anywhere in the world: