jars and pearls


1) 6 jars with pearls**
Sultan Oil-well decided that his beautiful daughter had reached the age of marriage, and of course numerous princes of the neighbouring states were interested in her hand.
Instead of choosing the handsomest or richest, he decided to choose the most intelligent candidate.

He put 6 jars in front of the assembled princes, and told them that each jar contained a number of pearls. Jar 2 contained 1 pearl more than jar 1; jar 3 had 1 pearl more than jar 2, and so on.
Then he ordered his daughter to take 1 pearl from jar 1 and put it in jar 2. Next she took 2 pearls from jar 2 and put it in jar 3, and so on, competing a complete circle by moving pearls from jar 6 into jar 1.
“Gentlemen” the sultan told the princes “jar 1 now has twice as many pearls as it had at start. How many pearls were in each jar at start?”

You can check your solution.

2) The boxes*
In one of his books (‘Test your wits’) Eric Doubleday presents the following, simplified version:
The daughter of the sultan had 4 boxes in front of her: each one contained one more than the previous one. The last one had twice as many as the first one.
What is the total number of pearls?

3) Men in a circle with shillings*
This one goes back to Lewis Carroll. It is one of his “pillow problems”, problems thought out during sleepless hours.

Some men sat in a circle, so that each had 2 neighbours. Each had a certain number of shillings. The first had 1 more than the second, who had 1 more than the third, and so on. The first gave 1 to the second, who gave 2 to the third, and so on, each giving 1 more than he received, as long as possible. There were then 2 neighbours, one of them had 4 times as much as the other.
How many men were there? And how many had the poorest at start?

Feel free to take the entire night to solve this one. Lewis Carroll solved them by head, and I’m sure that with some exercise you can too.

You can check your solution.

Incidentally, This blog is now slightly over 1 year old. The general speed has been 1 post in 2 weeks. I’m trying to move up speed to once a week, and I seem to have sufficient puzzles in store to keep up this pace during the month of May. I may have to slow down somewhere in the future again, but we’ll see that when we get there. As many posts contain more than 1 puzzle, the general pace of puzzles has been over 1 puzzle a week.

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