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Puzzle
- US Version
A magician charges a traveler with a task. "Take a certain number of pearls out of a bag of 500. This number, when divided by any number two through seven, always produces a whole number if you remove one pearl before dividing. Bring me this number, and all the pearls are yours."
The number of pearls the traveler takes from the bag doesn't produce a whole number when one pearl is removed and the remaining pearls are divided by four. But his number meets the other conditions. How many pearls did he take from the bag?
- UK Version
A wizard sets a traveller a strange task.
"There are 500 pearls in that cave. I want you to go and bring a certain number of pearls to me. This number allows you to divide the pearls into groups of 2, 3, 4, 5, 6 or 7 and always have one pearl left over. Bring me this number of pearls and you can keep them all for yourself!"
The traveller tries his best, but the number of pearls he bring back doesn't leave one pearl over when divided into groups of 4. How many pearls did he bring to the wizard?
Hints
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Solution
Incorrect
Too bad!
- US Version
This puzzle may seem like a pain to solve, but if you take the time to calculate everything out, there's really nothing difficult about it.
- UK Version
This puzzle may seem like a pain to solve, but if you take the time to calculate everything, there's really nothing difficult about it. There are also ways to reduce the amount of calculation you need to do.
Correct
Brilliant!
- US Version
The answer is 211 pearls. The magician essentially asked for the value one more than a value that, when divided by any number two through seven, produces a whole number. Any of these numbers divides neatly into 420, so when one is added to it, you get the magician's number: 421.
The number of pearls the adventurer had is a number that's neatly divided by any number from two through seven, except four. Adding one to that gets you your answer.
- UK Version
The answer is 211 pearls. The traveller's number must be between 1 and 500, and one more than a number that is divisible by 2, 3, 5, 6 and 7. The quickest way to find this number is to make a list of multiples of 7 up to the limit of 500, then see if those numbers are also divisible by the other numbers. This takes quite some time unless you realise that any number divisible by 6 is also divisible by 2 and 3, so you really only have to compare your multiples of 7 against 6 and 5. If only the traveller had brought back 421 pearls...
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