Can you make all of the numbers from 1 to 10 using the number 4 exactly four times? You can use +, –, x, ÷, √ (square root) and brackets as many times as you need to.
Solution 1:
There are many possibilities for some of these numbers. We will only give one answer here.
1 = (4 + 4) ÷ (4 + 4)
2 = (4 × 4) ÷ (4 + 4)
3 = (4 + 4 + 4) ÷ 4
4 = √4 × √4 × √4 ÷ √4
5 = (√4 × √4) + (4 ÷ 4)
6 = [(4 + 4) ÷ 4] + √4
7 = 4 + 4 – (4 ÷ 4)
8 = 4 + 4 + 4 – 4
9 = 4 + 4 + (4 ÷ 4)
10 = 4 × 4 – 4 – √4
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?