T he Main Challenge
This is a continuation of a number puzzle, posted on DAY 10, made famous by French writer, George Perec.
In that challenge, we asked you to use seven 7’s (7, 7, 7, 7, 7, 7 and 7) once each, with + – × and ÷ available, to make target numbers from 1 to 3.
To continue the puzzle, and make 4, you could simply do:
- 7 – 7÷7 – 7÷7 – 7÷7 = 4
We now invite you to make all the target numbers from 5 through to 9.
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.
The 1st & 6th rows contain the following fourteen numbers:
2 5 9 12 14 15 18 20 22 33 40 49 56 72
Which multiple of 8, when 7 is subtracted from it, becomes a square number?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every 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).
Show how you can make 180, in TEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 6 and 12 once each, with + – × ÷ available, which is the ONLY target number it is possible to make from the list below?
8 16 24 32 40 48 56 64 72 80
#8TimesTable
The Target Challenge
Can you arrive at 180 by inserting 4, 6, 8 and 10 into the gaps on each line?
- (◯+◯+◯)×◯ = 180
- (◯+◯)×(◯+◯) = 180
- ◯²+◯×(◯+◯) = 180
- (◯+◯+double◯)×◯ = 180
Answers can be found here.
Click Paul Godding for details of online maths tuition.
