T he Main Challenge
It is possible to use seven 4’s (4 4 4 4 4 4 and 4) once each, together with the four operations + – × ÷, to make all the different target numbers 1, 2, 3 and 4.
For instance, one way of arriving at the number 1 is:
4 – 4÷4 – 4÷4 – 4÷4 = 1
Can you show how to make the next three target numbers 2, 3 and 4?
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 4th & 7th rows contain the following fourteen numbers:
3 4 10 11 24 27 30 32 35 44 54 60 70 77
What is the sum of the multiples of 9?
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 FIVE ways of making 76 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 4, 6 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?
70 71 72 73 74 75 76 77 78 79
#NumbersIn70s
The Target Challenge
Can you arrive at 76 by inserting 6, 8, 10 and 12 into the gaps on each line?
- ◯×◯+(◯–◯)² = 76 (2 different ways)
- ◯×◯–(◯÷◯)² = 76
- ◯×(◯–◯)+◯² = 76
Answers can be found here.
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