Puzzles by Paul Godding

Paul’s Puzzles

By Paul Godding

The Main Challenge

Can you insert the numbers 1-9, exactly once each, into the gaps below so that all three lines work out arithmetically?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84. The 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80 Which number, when 20 is added to it, becomes a square number?

The Target Challenge

Can you arrive at 189 by inserting 3, 4, 5 and 7 into the gaps on each line? ◯×◯×(◯+◯) = 189 (◯+◯–◯)³+◯³ = 189

The Mathematically Possible Challenge

Using 3, 4 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#6TimesTable

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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). Show how you can make 189, in ELEVEN different ways, when using Lagrange’s Theorem.

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: