T he Main Challenge
Starting from 1, find the sum of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, nor are multiples of 3, 5 or 7.
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 4th & 6th rows contain the following fourteen numbers:
3 5 10 12 18 20 32 33 35 44 49 54 56 60
What is the sum of the multiples of 11?
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 FIVE ways of making 58 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 1, 6 and 7 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
5 10 15 20 25 30 35 40 45 50
#5TimesTable
The Target Challenge
Can you arrive at 58 by inserting 4, 6, 8 and 10 into the gaps on each line?
- ◯×◯–◯÷◯ = 58
- ◯²+◯+◯+◯ = 58
- ◯²–√(◯×(◯–◯)) = 58
Answers can be found here.
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