The Main Challenge
Lagrange’s Four-Square Theorem states that every integer can be made by adding up to four square numbers.
For example, 7 can be made by 2²+1²+1²+1² (4+1+1+1).
Show how you can make 31 when using Lagrange’s Theorem in TWO different ways.
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 1st & 4th rows of the playing board contain the following fourteen numbers:
2 3 9 10 14 15 22 32 35 40 44 54 60 72
What is the sum of the multiples of 5?
The Mathematically Possible Challenge
Based on our best-selling arithmetic board game.
Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 145 by inserting 3, 4, 5 and 8 into the gaps on each line?
- (◯×◯–◯)×◯ = 145
- (◯+◯)²–double(◯×◯) = 145
- (◯+◯)²+half(◯–◯) = 145
Answers can be found here.
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