T he Main Challenge
If you multiply a mystery number by 6 and then subtract 6, the result is the same as if you first multiplied the same mystery number by 3 and then added 3.
Is the value of this mystery number 1, 2, 3, 4 or 5?
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 & 4th rows contain the following fourteen numbers:
3 10 13 25 32 35 36 42 44 45 54 60 66 80
What is the sum of the multiples of 7 listed?
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 just THREE ways of making 112 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 1, 4 and 9 once each, with + – × ÷ available, which TWO numbers is it 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 112 by inserting 3, 5, 10 and 11 into the gaps on both lines?
- ◯×◯+◯–◯ = 112
- (◯+◯)×(◯–◯) = 112
Answers can be found here.
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