The Main Challenge
Using the numbers 4, 5 and 6 once each, together with + – × ÷, which THREE target numbers from the following list are NOT mathematically possible to make?
2 3 4 5 6 7 10 12 14 15 19 20 26 29 30
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 3rd & 7th rows contain the following fourteen numbers:
4 11 13 24 25 27 30 36 42 45 66 70 77 80
What is the difference between the highest and lowest multiples of 7?
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 FIVE ways of making 50 when using Lagrange’s Theorem. Can you find them all?
The Mathematically Possible Challenge
Using 8, 9 and 10 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 50 by inserting 2, 5, 10 and 20 into the gaps on each line?
- ◯²–◯×◯÷◯ = 50
- (◯+◯)×◯+◯ = 50
- ◯⁵+◯–◯÷◯ = 50
Answers can be found here.
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