T he Main Challenge
When playing Mathematically Possible, players must analyse which numbers can (or can’t) be made from the three numbers rolled on their dice.
Using the numbers 3, 4 and 6, with + – × ÷ available, which THREE of the following target numbers are NOT mathematically possible to achieve?
1 2 3 5 6 7 8 10 12 13 14 18 21 22 24 27 30
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 4th & 5th rows of the playing board contain the following fourteen numbers:
3 6 7 10 16 21 32 35 44 50 54 60 81 84
What is the difference between the sum of the multiples of 5 and sum of the multiples of 6?
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).
Show how you can make 193, in EIGHT different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 4 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?
12 24 36 48 60 72 84 96 108 120
#12TimesTable
The Target Challenge
Can you arrive at 193 by inserting 7, 10, 11 and 13 into the gaps on each line?
- ◯×(◯+◯)+◯ = 193
- ◯²+◯²+◯+◯ = 193
Answers can be found here.
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