# How many pearls are there in the sack?

By matrixx

@matrixx (254)

April 23, 2007 9:47am CST

A king and queen had 11 sons. Once a royal family from bordering country visited them. They brought with them a gift for the King, a sack full of pearls. King handed that over to his eldest son to distribute as per his wish among all his brothers. The prince thought to keep it for himself but he was caught, by the next eldest son, hiding the sack. They decided to distribute the pearls equally between them but when counted there was 1 pearl left undecided. The 3rd prince was passing by when he over heard them. He immediately understood what was happening and demanded that the pearls be equally distributed among 3 princes. they counted the pearls, still 1 pearl remained undecided. similarly up till 10th prince, there was always 1 pearl undecided but when 11th claimed his share and they distributed; all pearls were distributed evenly among 11 princes.
how many pearls were there in the sack? First to answer correctly wins the best response:-)

1 person likes this

7 responses

@matrixx (254)

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23 Apr 07

no sorry! when we try to divide 121 in 7 princes, there will be 2 pearls undecided, similarly 4 undecided in case of 9 princes while the condition is 1 pearl should remain undecided before 11th prince.
why are you giving up so quickly, try you can get it:-)

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@matrixx (254)

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23 Apr 07

oh mahmah! I am really so sorry to cause you headache. please accept my apologies. I'll wait for someone to answer it, other wise i'll tell the answer maximum by tomorrow. If no one could get this brain teaser, i'll offer a gift of best response to you for the pain i caused as well as your effort. I am really sorry again.

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@racheld (840)

• United States

23 Apr 07

I believe there are 1441 pearls. I knew the answer had to be a multiple of eleven. I knew the number that was being multiplied by 11 had to be ending in a 1 because there was one left. So with a lot of trial and error I came across 11 * 131 = 1441. Am I right because like the other person said, this was giving me a headache but I became addicted to finding the answer! :)

@matrixx (254)

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24 Apr 07

Racheld! you have really tried and went to some length but unfortunately answer is not right since it wroks weel upto 6 princes but when 7th will come, the remainder will not be 1 but it will be 6, so it will not fit the conditions. thanks for trying, and you can still try:-)

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@kamran12 (5555)

• Pakistan

23 Apr 07

There were 25201 pearls in the sack. I wonder how big the sack would be to house so many pearls or how small the pearls would be to fit in a sack:-) I am sure about the answer, since it is purely mathematical. Divide the above number from 2 to 10 and you will get remainder equal to 1 and when it is divided by 11, we will get a remainder equal to 0, hence evenly distributing the pearls among 11 princes. Am i right?

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@kamran12 (5555)

• Pakistan

24 Apr 07

Thanks matrixx! that you appreciated my effort. Hey! that's not fair, you didn't ask for expalnation as a condition for best response, but i'll explain anyway:-) you know, to get remainder equal to 1 when dividing from 2-10 we need to have a LCM of 2-10 plus 1. According to mathematical logic that number should end in 1 otherwise it won't satisfy for example to have remainder equal to 1 when dividing by 10 there should be 1 at the end, right! now 1 as end digit can only be achieved by multiplying 11 with a number which itself end in 1. Now i took the LCM, multiplied it with arbitrary numbers starting from 1 then added 1 to this number then divided it by 11. so in 10 tries i got the number:-) I think it's clear now.
Having explained that, i must say this is the hardest i did on mylot till date:-) it really took more than 20 minutes to solve. and yes i am really honored that you requested friendship:-) Thanks anyway, i enjoyed doing it.

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@LilyoftheThorns (12925)

• United States

23 Apr 07

Aw man! you beat me. I was going to guess 11! lol. I think it is right. Good job!

@Jmoss1806 (98)

• United States

23 Sep 07

I don't have a clue but its either a really LARGE number or a really small number. lol My head hurts trying to think about it