T he Main Challenge
Read the following facts below about a particular number:
- It is a 2-digit number,
- It is an even number,
- When the two digits are added together they make another 2-digit even number that is also a square number.
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 1st & 7th rows contain the following fourteen numbers:
2 4 9 11 14 15 22 24 27 30 40 70 72 77
What is the difference between the sum of the multiples of 11 and the sum of the multiples of 10?
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 SIX ways of making 121 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 4 and 12 once each, with + – × ÷ available, which are the only TWO numbers it is 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 121 by inserting 4, 5, 6 and 7 into the gaps on each line?
- (◯+◯)×(◯+◯) = 121
- (◯+◯)²×(◯–◯) = 121
- ◯³–◯×(◯–◯) = 121
Answers can be found here.
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