[DB064] Stones in a Vase

064 - Stones in a Vase

Stones in a Vase is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

"This vase holds 101 stones, each identical in size and feel. There are 50 black stones and 51 white stones. Now, put on this blindfold, reach in, and pull out as many stones as you like. When you're finished, if you've removed an equal number of black and white stones, you'll receive a number of gold pieces equal to the number of stones you pulled out."

How many stones should you remove to give yourself the best chance of removing equal numbers of stones while getting the most money possible?

UK Version

"This vase holds 101 stones, each identical in size and feel. There are 50 black stones and 51 white stones. Now, put on this blindfold, reach in, and pull out as many stones as you like. When you're finished, if you've removed an equal number of black and white stones, you'll receive a number of gold coins equal to the number of stones you pulled out."

How many stones should you remove to give yourself the best chance of getting the most money possible?

Hints

Click a Tab to reveal the Hint.

Since the stones are of the same size and feel, there is absolutely no way to tell them apart while removing them.

US Version

The best chance you'll have at pocketing those coins is just around 50 percent.

There's no way of ensuring you'll win the coins.

UK Version

The chances of you winning those coins are about 50/50.

There's no way of ensuring that you'll win the coins.

Let's think about this for a moment.

US Version

Whether you pull out two stones or 100 stones, your chances of winning the gold are the same: just about 50 percent.

UK Version

Whether you pull out two stones or 100 stones, your chances of winning the gold are the same: 50/50.

Solution

Incorrect

Too bad!

In situations like this one, it pays to go for the big money, so don't hold back!

Correct

Well done!

US Version

If you remove 100 stones from the vase, only one will remain inside. If that remaining stone is white, it means you've successfully removed 50 stones of each color. Of course, removing just two stones would give you the same chance of winning the coins as removing 100 stones, but the amount of money you receive for successfully removing 100 stones dwarfs the reward you'd receive for two stones.

UK Version

If you remove 100 stones from the vase, only one will remain inside. If that remaining stone is white, it means you've successfully removed 50 stones of each colour. Of course, removing just two stones would give you the same chance of winning the coins as removing 100 stones, but the amount of money you receive for successfully removing 100 stones dwarfs the reward you'd receive for two stones.

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