T he Main Challenge
By following these rules, list SEVEN different positive whole numbers that total 100:
- each number must be at least 4 away from its nearest neighbour,
- the list must contain at least three square numbers.
Can you find at least one solution?
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 6th & 7th rows contain the following fourteen numbers:
4 5 11 12 18 20 24 27 30 33 49 56 70 77
What is the sum of the multiples of 4?
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 92 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 5, 7 and 10 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?
5 10 15 20 25 30 35 40 45 50
#5TimesTable
The Target Challenge
Can you arrive at 92 by inserting 2, 4, 10 and 12 into the gaps on each line?
- ◯×◯×◯+◯ = 92
- ◯²–(◯+◯)÷◯ = 92
- ◯×(◯–◯)–◯= 92
Answers can be found here.
