Raskina I.V.

The inhabitants of the Island of Misfortune, like us, divide the day into several hours, an hour into several minutes, and a minute into several seconds. But they have 77 minutes in a day and 91 seconds in an hour. How many seconds are there in a day on the Island of Misfortune?
If you divide 77 by the number of minutes in an hour, you get the number of hours in a day. If you divide 91 by the number of minutes in an hour, you get the number of seconds in a minute. This means that both 77 and 91 are divisible by the number of minutes in an hour. GCD(77, 91) = 7. Since there is more than one minute in an hour, there must be 7 minutes in an hour—no other number greater than one divides both 77 and 91. Then, in a day, there are $77: 7=11$ hours and $11 \cdot 91=1001$ seconds.

## Otvet

1001 seconds.