Can you make all of the numbers from 1 to 10 using each of the numbers 1, 2, 3, 4 once and only once? You can use +, –, x, ÷ and brackets as many times as you need to.
For example, 4 = (4 – 2) × (3 – 1)
Solution 1:
There are many possibilities for some of these numbers. We will only give one answer here.
1 = (2 – 1) ÷ (4 – 3)
2 = 2 × (4 – 3) ÷ 1
3 = [2 + (4 – 3)] ÷ 1
4 = (4 – 2) × (3 – 1)
5 = (4 + 3 – 2) × 1
6 = 4 + 3 – 2 + 1
7 = (4 + 3) × (2 – 1)
8 = 4 + 3 + 2 – 1
9 = (4 + 3 + 2) × 1
10 = 4 + 3 + 2 + 1
Extension:
(i) How many of the numbers from 11 to 100 can you make this way?
(ii) How many ways can you find to produce each of these numbers?