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Leaky Tank is a puzzle in the UK version of Professor Layton and the Curious Village.

## Puzzle

A 2.5m deep water tank has water poured into it for 8 hours, starting at 9am. The water level rises by 60cm in this time. However, it seems that water is leaking out again at night, because the next morning the water level has dropped by 20cm.

If the water level continues to rise 40cm a day in this way, on what day will the tank first overflow?

## Hints

Click a Tab to reveal the Hint.

The total rise in water level each day is 40cm, just as the puzzle says.

But if you think about it, isn't there an important point missing?

Yes, you're on the right track now.

In 8 hours starting at 9am - in other words, until 5pm - water enters the tank and the water level rises by 60cm.

For the next 16 hours, water leaks out of the tank, bringing the water level down by 20cm.

At 5pm on day 1, the water level is 60cm.
At 9am on day 2, it's 40cm.
At 5pm on day 2, 1m.
At 9am on day 3, 80cm.
At 5pm on day 3, 1.4m.
At 9am on day 4, 1.2m.

Notice anything?

## Solution

### Correct

That's right! The answer is the 6th day.

It's easy to fall into the trap of thinking that because the water level rises by 40cm each day, it will have risen to 2.40m by the 6th day, and therefore overflow the 2.5m deep tank on the 7th day. However, on the 6th day the water level actually starts at 200cm and rises by 60cm over the course of the day, overflowing the tank.

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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