T he Main Challenge
Here’s a number trail involving 16 arithmetical steps. Start with the number 2, then:
- +33
- divide by seven
- ×3
- add ten percent
- double this
- add three
- find the square root of this
- +7
- 1/2 of this
- add nineteen point five
- subtract two
- ÷6
- +15
- ×5
- –93
- ÷2
What is your final answer?
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 & 6th rows contain the following fourteen numbers:
5 12 13 18 20 25 33 36 42 45 49 56 66 80
Which two numbers, when doubled, are also present 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 SEVEN ways of making 135 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 3, 6 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
10 20 30 40 50 60 70 80 90 100
#10TimesTable
The Target Challenge
Can you arrive at 135 by inserting 4, 5, 9 and 12 into the gaps on each line?
- ◯²–◯×(◯–◯) = 135
- ◯×◯×◯÷◯ = 135
- (◯+◯)²+half(◯×◯) = 135
Answers can be found here.
Click Paul Godding for details of online maths tuition.
