T he Main Challenge
This is the 3rd and final part of a number puzzle posted initially on DAY 10, then on DAY 180, and made famous by French writer, George Perec.
The challenge involves using seven 7′s (7, 7, 7, 7, 7, 7 and 7) once each, with + – × and ÷ available, to make various target numbers.
For instance, to make 9 in the previous challenge on DAY 180, you could have done:
- [7 + (7÷7) + (7÷7)] × (7÷7) = 9
Up until now, it has been possible to make every target number from 1 through to 9 with seven 7’s, so for today’s time-consuming task:
Part 1: Show how to make all target numbers from 10 through to 19.
Part 2: Which is the first number after 19 that is impossible to make with seven 7’s?
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 2nd & 3rd rows contain the following fourteen numbers:
8 13 17 25 28 36 42 45 48 55 63 64 66 80
Which two numbers have a difference of 13?
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 190, in EIGHT different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 4 and 12 once each, with + – × ÷ available, which SIX numbers is it 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 190 by inserting 4, 5, 6 and 14 into the gaps on each line?
- (◯+◯)×(◯+◯) = 190
- (◯×◯+◯)×◯ = 190
- ◯²–◯×(◯–◯) = 190
Answers can be found here.
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