11.1. At first, there were natural numbers, from 1 to 2021. And they were all white. Then the underachiever Borya painted every third number blue. Then the top student Vova came and painted every fifth number red. How many numbers remained white? (7 points)

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# Solution

Borya repainted the numbers divisible by 3, a total of [2021:3]=673 numbers. Vova repainted [2021:5]=404 numbers. 673+404=1077. However, numbers divisible by 15 were counted twice. [2021:15]=134. Therefore, the number of white numbers remaining is 2021-1077+134=1078.

Answer: 1078 white numbers

| criteria | points |
| :--- | :---: |
| 1. correct solution | 7 |
| 2. Not accounted for numbers divisible by 15 being counted twice. | 4 |
| 3. For each arithmetic error | 1 |