T he Main Challenge
It is possible to use seven 5’s (5 5 5 5 5 5 and 5) once each, with the four operations + – × ÷, to make all the target numbers from 1 to 5.
For instance, to arrive at the target numbers 1 and 2, you can do:
- [(5+5)÷5 – 5÷5] × 5÷5 = 1
- [(5+5)÷5 – 5÷5] + 5÷5 = 2
Your task is to show how to arrive at the other target numbers 3, 4 and 5.
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 5th & 7th rows contain the following fourteen numbers:
4 6 7 11 16 21 24 27 30 50 70 77 81 84
What is the product of the two prime numbers listed?
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 SIX ways of making 137 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 3, 6 and 10 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 137 by inserting 4, 5, 6 and 8 into the gaps on each line?
- ◯³+◯²+◯×◯ = 137
- ◯³+◯×◯÷◯ = 137
Answers can be found here.
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