T he Main Challenge
When a certain 4-digit number is multiplied by 4, its digits appear in reverse order. It also has both of these properties:
- its first digit is a quarter of the last one, and
- its second digit is one less than the first.
What number must it be?
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 2nd & 6th rows contain the following fourteen numbers:
5 8 12 17 18 20 28 33 48 49 55 56 63 64
List four pairs of numbers that have a difference of 7.
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 THREE ways of making 41 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 6 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
1 8 25 64 125
#CubeNumbers
The Target Challenge
Can you arrive at 41 by inserting 3, 5, 7 and 9 into the gaps on each line?
- ◯×◯+◯–◯ = 41
- (◯+◯)×◯–◯ = 41
- (◯–◯)×◯+◯ = 41
