T he Main Challenge
Using the numbers 3, 4 and 5 just once each, and with + – × ÷ available, only FOUR of the numbers on the list below are possible to achieve. Which ones are they?
1 3 6 9 10 12 15 18 21 24 27 30
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 & 7th rows contain the following fourteen numbers:
2 4 9 11 14 15 22 24 27 30 40 70 72 77
Which multiple of 5, when subtracting 4 from 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 SEVEN ways of making 125 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 4 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?
2 3 5 7 11 13 17 19 23 29
#PrimeNumbers
The Target Challenge
Can you arrive at 125 by inserting 5, 10, 15 and 20 into the gaps on each line?
- ◯×◯+◯+◯ = 125
- ◯×◯–◯×◯ = 125
- ◯²–◯×(◯–◯) = 125
- (◯+◯)×(◯–◯) = 125
- ◯×◯+◯+double◯ = 125
Answers can be found here.
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