## Missing Weight

#### Problem

The weights of ten boys are recorded in a stem and leaf diagram.

Weight (kg) 4

5

6

77

2 4 7 9

1 4 6 8

2

Key: | 5 | 2 means 52 kg |

Although the mean of the data is correct, two of the entries had their digits reversed and 75 kg was accidentally written down as 57 kg. Given that the 47 kg is not really the minimum weight, how heavy is the lightest boy?

#### Solution

The sum of the data in the stem and leaf diagram is 600. If 57 kg is incorrect, 600 57 = 543 and 543 + 75 = 618. As the mean is correct, the new total should also be 600, therefore the difference between the other incorrect value and the reverse of its digits must be 18. As we need to lose 18, the incorrect number must be greater than its reverse and the difference between the digits must be 2.

We can see that 64 has this property. That is, 618 64 = 554 and 554 + 46 = 600 and so we deduce that the lightest boy weighs 46 kg.

Why did the difference between the digits have to be 2?

Investigate the difference between a 2-digit number and its reverse.