## 1. Jaja

Baka Mara has four hens. The first hen lays one egg every day. The second hen lays one egg every other day. The third hen lays one egg every third day. The fourth hen lays one egg every fourth day. If on January 1, 2023, all four hens laid one egg, how many eggs in total will Baka Mara's hens lay throughout the entire year of 2023?

## Result: $\quad 762$
## First solution.

The year 2023 is not a leap year, so it has 365 days.

The first hen, which lays one egg every day, will lay 365 eggs in the entire year.

If we divide 365 by 2, the quotient is 182 and the remainder is 1. This means that in the entire year, there are 182 times two days and one additional day. Since the second hen lays an egg every other day, she will lay a total of $182+1=183$ eggs in 364 days. Since $365 : 3 = 121$ with a remainder of 2, this means that in the entire year, there are 121 times three days and two additional days, so the third hen will lay $121+1=122$ eggs.

Since $365 : 4 = 91$ with a remainder of 1, the fourth hen will lay $91+1=92$ eggs.

All four hens together will lay $365+183+122+92=762$ eggs.