Paul’s Puzzles By Paul Godding The Main Challenge
The Lagrange Challenge
Allocate each letter of the English alphabet a numerical value, A=1 B=2 C=3 . . . Z=26. When adding the individual letters, find the total value of these four important words: • • • •
KNOWLEDGE HARD WORK RESILIENCE ATTITUDE
There are TWO ways of making 71 when using Lagrange’s Theorem. Can you find both?
The Mathematically Possible Challenge Using 4, 6 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below? 8 16 24 32 40 48 56 64 72 80 #8TimesTable
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 1st & 6th rows contain the following fourteen numbers: 2 5 9 12 14 15 18 20 22 33 40 49 56 72
The Target Challenge Can you arrive at 71 by inserting 3, 5, 7 and 9 into the gaps on each line? • • •
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).
◯×◯+◯+◯ = 71 ◯²+◯×◯–◯ = 71 (◯+◯)×◯–◯² = 71
Which six numbers listed can each be made by adding three others from the list?
*** 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: 07970868121 from within Wales and the UK, or +447970868121 from the rest of the world. - 45 -
