T he Main Challenge
From the numbers below, eliminate all:
- square numbers,
- triangular numbers,
- multiples of 4 and
- factors of 70.
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25
Which is the only number left remaining?
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 1st & 5th rows contain the following fourteen numbers:
2 6 7 9 14 15 16 21 22 40 50 72 81 84
What is the difference between the lowest and highest multiples of 5?
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 THREE ways of making 53 when using Lagrange’s Theorem. Can you find them?
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?
70 71 72 73 74 75 76 77 78 79
#NumbersIn70s
The Target Challenge
Can you arrive at 53 by inserting 4, 4, 5 and 6 into the gaps on each line?
- (◯+◯)×◯+◯ = 53
- ◯²+◯×◯+◯ = 53
- ◯²×◯–(◯+◯) = 53
Answers can be found here.
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