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Delivering wine

Delivering wine

Three friends bought a box full of wine bottles from a street vendor. At the time of making the distribution they saw that the box contained 21 equal bottles of which only 7 were fully filled. There were 7 others that were exactly in the middle and another 7 empty.

Despite the scam, they decided to distribute the wine and bottles among all so that each one took the same amount of wine and bottles. Since curiously the bottles were perfectly closed they wanted to make the distribution without opening any.

Can you think of how the 21 bottles can be distributed so that each one receives the same number of bottles and the same amount of wine without opening any bottles?

Solution

There are two possibilities. The first cast would be:

  • The first friend takes 3 full bottles, 1 half full and 3 empty.
  • The second is left with 2 full bottles, 3 half full and 2 empty.
  • The third friend has 2 bottles full, 3 half full and 2 empty.

Another possibility would be:

  • The first friend takes a full bottle, 5 half full and 1 empty.
  • The second one is left with 3 full bottles, 1 half full and 3 empty.
  • The third friend has 3 bottles full, 1 half full and 3 empty.