Puzzles by Paul Godding

Paul’s Puzzles

By Paul Godding

The Main Challenge

Today’s task is to arrive at the target number Here’s a mini-Mathelona challenge where you must place the eight digits 0, 1, 1, 2, 2, 2,3 and 4 into the eight gaps so both lines work out arithmetically: ◯ + ◯ = 4 = ◯ × ◯ ◯ – ◯ = 2 = ◯ ÷ ◯

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 (4+1+1+1). Show how you can make 162, in THIRTEEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using the three digits 3, 5 and 8 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1 8 27 64 125

#CubeNumbers

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 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

Which two numbers, when each is divided by 6, also appear on the list?

The Target Challenge

Can you arrive at 162 by inserting 2, 3, 9 and 12 into the gaps on each line? • ◯×◯×(◯–◯) = 162 • ◯³×(◯×◯–◯) = 162

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: