T he Main Challenge
This describes a particular number less than 100:
- its digits add up to 12,
- if the unit digit is subtracted from the tens digit, then doubled, the answer is also 12.
What is the number?
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
List THREE different numbers that have a sum of 77.
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 111 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 1, 4 and 9 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
9 18 27 36 45 54 63 72 81 90
#9TimesTable
The Target Challenge
Can you arrive at 111 by inserting 2, 3, 5 and 7 into the gaps on both lines?
- (◯×◯+◯)×◯ = 111
- (◯+◯)²+double(◯×◯) = 111
Answers can be found here.
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