T he Main Challenge
Using the numbers 3, 5 and 5 once each, with + – × ÷ available, which FOUR numbers from the following list are NOT mathematically possible to make?
1 2 3 4 7 10 13 15 18 20 22 25 28 30
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 difference between the two prime numbers on the list?
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 FOUR ways of making 94 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 5, 7 and 10 once each, with + – × ÷ available, which TWO numbers it is possible to make from the list below?
7 14 21 28 35 42 49 56 63 70
#7TimesTable
The Target Challenge
Can you arrive at 94 by inserting 3, 5, 7 and 10 into the gaps on each line?
- ◯³–◯×◯–◯= 94
- ◯²–◯×(◯–◯) = 94
- ◯²+◯×(◯+◯)= 94 (2 different ways)
Answers can be found here.
