T he Main Challenge
You’ve rolled the numbers 2, 3 and 4 with three dice. Using these once each, with + – × ÷ available, what is the lowest positive whole number it is NOT possible to make?
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
Which three different numbers have a sum of 100?
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 FOUR ways of making 36 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 6 and 11 once each, with + – × ÷ available, which THREE numbers is it 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 36 by inserting 2, 3, 4 and 6 into the gaps on each line?
- (◯+◯+◯)×◯ = 36
- (◯²+◯)×◯÷◯ = 36
- (◯–◯)×◯×◯ = 36
- ◯²×(◯+◯–◯) = 36 (2 different ways)
Answers can be found here.
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