The Main Challenge
The smallest positive integer that has exactly three factors is FOUR; these are 1, 2 and 4. Find the next integer to have just three factors and the product of these three numbers.
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 3rd & 7th rows contain the following fourteen numbers:
4 11 13 24 25 27 30 36 42 45 66 70 77 80
What is the sum of the multiples of 10?
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 TWO ways of making 46 when using Lagrange’s Theorem. Can you find both?
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?
7 14 21 28 35 42 49 56 63 70
#7TimesTables
The Target Challenge
Can you arrive at 46 by inserting 3, 4, 5 and 9 into the gaps on each line?
- (◯+◯)×◯+◯ = 46
- ◯²+◯×◯+◯ = 46
- ◯×◯+◯–√◯ = 46
Answers can be found here.
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