T he Main Challenge
Group these ten numbers into five pairs so that the difference between the two numbers in each pair is divisible by 7:
6 17 28 37 45 58 64 78 83 98
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 3rd & 6th rows contain the following fourteen numbers:
5 12 13 18 20 25 33 36 42 45 49 56 66 80
From the list, what is the sum of the multiples of 7?
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 133 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 3, 6 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
8 16 24 32 40 48 56 64 72 80
#8TimesTable
The Target Challenge
Can you arrive at 133 by inserting 10, 11, 13 and 20 into the gaps on each line?
- ◯×◯+◯–◯ = 133
- ◯×◯+√(◯–◯) = 133
Answers can be found here.
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