# 5.1. Condition:

On Monday, Olya started training according to the following program: 6 days of training in a row, then 2 days of rest, then again 6 days of training, 2 days of rest, and so on. On which day of the week will the hundredth training session fall?

## Answer options:

$\square$ Monday

$\square$ Tuesday

$\square$ Wednesday

$\square$ Thursday

$\square$ Friday

$\square$ Saturday

$\square$ Sunday
# Solution.

Let's try to understand which cycle of the program (i.e., an 8-day segment consisting of 6 training days and 2 rest days) the hundredth training session falls on (not the hundredth day of the program). By dividing 100 by 6, we can determine how many cycles must pass before the hundredth training session—16 with a remainder of 4. This means that 16 cycles will be complete, and four more training days will pass before reaching the hundredth training session: $16 \cdot(6+2)+4=132$ days. To find the day of the week, we need to look at the remainder when dividing by 7. Dividing 132 by 7 gives a remainder of 6, which means the day of the week is Saturday.