Water Jar Problem

[mafou]

This problem involves three jars with specific capacities (and, important, no gradations), and you are required to indicate how you would measure (obtain) a specified amount of water.

For example:

You are given jars holding 21, 127, and 3 quarts, respectively. You are aked to indicate how to measure out exactly 100 quarts.

Go for it!

[Ghazali]

fill up the 127 to its capacity, pour this into filling the 21 and then the same for the 3, then empty it. then again into the 3 you got 100 left in the 127 jar.

[mafou]

This task requires you, the problem solver, to arrange a deck of playing cards so that, when one alternates between placing the top card on the table and moving the top card to the bottom of the deck, a specified order of cards will be placed on the table.

For example:

Suppose you are to arrange the cards Ace through 8 so that, following the alternation scheme described above, the cards are placed on the table in the order A, 1,2,3,4,5,6,7,8.

How do you accomplish this task?

[Mary Zimmermann]

The way to accomplish this is to arrange the deck in the order A,5,2,7,3,6,4,8.

To realize this, for example, the first four cards placed on the table must be in the 1st, 3rd, 5th, and 7th positions in the deck, and so on.

Transfer tasks would pose different card-arrangement problems, for example, arranging four red and four black cards so that, when alternated, as above, the order produced would be RBRBRBRB (the soultion is RRBRRBBB).