The Coin Box Problem

 

 

As a collector of rare coins, you have a special cabinet with 16 numbered compartments (as shown above). Each compartment contains the same number of coins as what is shown on the label. At least it did, until somebody mixed up your coins, so that now no compartment holds the same number of coins as what is shown on the label. Each drawer still holds a different number of coins, from one to sixteen, just not what is on the label. Can you figure out, from the following clues, the new arrangement?

1) The compartment with three coins now lies directly above the compartment with sixteen coins.

2) The new number of coins in one compartment is the square of the old number, and it is directly above a compartment with twice as many coins in it now than it used to have.

3) The compartment which now has two coins is not in the left-most column.

4) One of the compartments now has half as many coins as it had before. It is directly below a compartment which now has twice as many coins as before, and above a compartment which has one less coin than before.

5) The compartment which now holds thirteen coins lies directly to the right of the compartment which now holds fifteen coins.

6) Following one of the two diagonals: one compartment now has nine less coins, the next has ten less, the next has twice as many as it started with, the last has nine more.

7) The compartment now containing six coins lies directly below the compartment which used to contain six coins.