T he Main Challenge
From the numbers 1 to 20 inclusive, find the only one that remains when all square numbers, multiples of 6, factors of 40 and odd numbers are eliminated.
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 & 6th rows contain the following fourteen numbers:
2 5 9 12 14 15 18 20 22 33 40 49 56 72
How many square numbers are present?
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 72 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 4, 6 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?
9 18 27 36 45 54 63 72 81 90
#9TimesTable
The Target Challenge
Can you arrive at 72 by inserting 4, 6, 8 and 10 into the gaps on each line?
- ◯×◯+◯+◯ = 72
- ◯×◯–(◯+√◯) = 72
- (◯+◯)×◯+◯ = 72
Answers can be found here.
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