T he Main Challenge
You are playing our Mathematically Possible board game and have rolled the numbers 6, 6 and 6 with your three dice. Using these once each, with + – × ÷ available, which SIX target numbers from 1-30 is it possible to make?
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 & 5th rows contain the following fourteen numbers:
6 7 13 16 21 25 36 42 45 50 66 80 81 84
What is the difference between the sum of the multiples of 7 and the sum of the multiples of 9?
The Lagrange 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 (or 4+1+1+1).
Show how you can make 172, in EIGHT different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 4, 6 and 10 once each, with + – × ÷ available, which are the SIX target numbers it’s possible to make from the list below?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 172 by inserting 3, 4, 5 and 8 into the gaps on each line?
- (◯+◯×◯)×◯ = 172
- (◯+◯)²+◯²+◯ = 172
Answers can be found here.
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