T he Main Challenge
Which is the ONLY way to make 38 when adding together SIX unique digits from 1-9?
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 4th & 5th rows contain the following fourteen numbers:
3 6 7 10 16 21 32 35 44 50 54 60 81 84
Which number, when 5 is added to it, becomes a square 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 FOUR ways of making 87 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 3 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 87 by inserting 3, 4, 6 and 7 into the gaps on each line?
- ◯×◯×√◯+◯ = 87
- ◯²×(◯+◯)–double◯ = 87
- (◯+◯)²+double(◯–◯) = 87
Answers can be found here.
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