The Main Challenge
Which is the lowest whole number that is NOT a multiple of 4, 5 or 6, nor a prime number, square number or cube number?
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 2nd & 4th rows contain the following fourteen numbers:
3 8 10 17 28 32 35 44 48 54 55 60 63 64
Which odd number, when 1 is subtracted from it, becomes a prime number?
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 TWO ways of making 21 when using Lagrange’s Theorem. Can you find both?
The Mathematically Possible Challenge
Using 5, 6 and 8 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 21 by inserting 3, 4, 5 and 6 into the gaps on each line?
- (◯+◯–◯)×◯ = 21
- ◯×◯+√(◯+◯) = 21
- ◯²–(◯×◯÷◯)² = 21
Answers can be found here.
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