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:
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:
◯ + ◯ = 4 = ◯ × ◯ ◯ – ◯ = 2 = ◯ ÷ ◯
3 5 10 12 18 20 32 33 35 44 49 54 56 60
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 #CubeNumbers
8
27
64
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? • •
125
◯×◯×(◯–◯) = 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:
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