Subject 4. A student has 15 red pencils and 22 black ones. Each day he loses 2 pencils. If he loses two pencils of the same color, he buys one black pencil on the same day, and if he loses one red and one black pencil, he buys one red pencil.

a. On which day will he be left with only one pencil?

b. What color will the last remaining pencil be?

## Note: All questions are mandatory

Time allowed: 2 hours

## MATHEMATICS OLYMPIAD  LOCAL STAGE  JANUARY 30, 2015

## GRADE 5

Scoring Guide
## Subject 4.

| a. | Every day he loses 2 pencils but buys 1, so at the end of the day he has one less pencil than the previous day. At the end of the 36th day, he is left with only one pencil | $\mathbf{3 p}$ |
| :--- | :--- | :---: |
| b. | If he loses 2 red or 2 black pencils, he buys a black pencil $\Rightarrow$ the number of red pencils does not change or decreases by 2. If he loses one red and one black pencil, he buys a red pencil $\Rightarrow$ the number of red pencils does not change. In both cases, the number of black pencils changes by 1 (either added or subtracted). The initial number of red pencils is 15, an odd number, so when he is left with only one pencil, it is red | $\mathbf{4 p}$ |