T he Main Challenge
In all four groups below, it is possible to make 24 by using the four numbers once each, with + – × ÷ available. Can you show how to achieve the target number of 24 in each case?
- 3 3 3 3
- 4 4 4 4
- 5 5 5 5
- 6 6 6 6
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
What is the sum of the multiples of 6 listed above?
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 just TWO ways of making 40 when using Lagrange’s Theorem. Can you find them both?
The Mathematically Possible Challenge
Using 2, 6 and 11 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
70 71 72 73 74 75 76 77 78 79
#NumbersIn70s
The Target Challenge
Can you arrive at 40 by inserting 2, 4, 5 and 10 into the gaps on each line?
- (◯+◯–◯)×◯ = 40
- (◯–◯)×◯×◯ = 40
- ◯²×◯²×◯÷◯ = 40
Answers can be found here.
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