T he Main Challenge
Firstly, allocate each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26. If the value of the word DOG is 26 by calculating 4+15+7, for example, which TWO of the following 3-letter words have the same value?
AXE AND BUT COT EAR MOP SAW TOP WOK ZOO
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.
The 1st & 4th rows contain the following fourteen numbers:
2 3 9 10 14 15 22 32 35 40 44 54 60 72
How many square numbers are present on the list?
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 38 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 6 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
30 31 32 33 34 35 36 37 38 39
#NumbersIn30s
The Target Challenge
Can you arrive at 38 by inserting 4, 6, 8 and 10 into the gaps on each line?
- ◯×◯+◯–◯ = 38
- ◯²–◯²–◯+◯ = 38
- ◯²+◯+◯–◯ = 38
Answers can be found here.
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