$\left[\begin{array}{l}[\text { Modular arithmetic (other) })] \\ {[\text { Word problems (other). }]}\end{array}\right]$

In a store, there were 6 boxes weighing 15, 16, 18, 19, 20, and 31 kilograms, respectively. Two companies bought five boxes, with one company taking twice as much by weight as the other. Which box was left in the store?
The mass of the purchased apples is divisible by 3.

## Solution

The total mass of all purchased apples is three times the mass of apples purchased from the first company, meaning it is divisible by 3. The total mass of all boxes gives the same remainder when divided by 3 as the sum of $0+1+0+1+2+1$ = 5. Therefore, the mass of the remaining box gives a remainder of 2 when divided by 3. There is only one such box.

## Answer

The box with a mass of 20 kg.