# 3 persons are to divide among themselves 21 equal cask, of which 7 are full, 7 are half full, and 7 are empty. how can an equitable division be made, without pouring the wine from any cask into any other, in such a way that each person receives the same amount of wine and the same total number of casks? is there more than one way to accomplish this division

## there are 7(1+1/2) = 21/2 casks of wine

Each person must thus get 7/2 = 3 1/2 casks

So, give 3 full and 1 half casks to two people, leaving

1 full and 5 half casks (3 1/2) for the 3rd person

## To find an equitable division where each person receives the same amount of wine and the same total number of casks, without pouring the wine from any cask into any other, we can follow these steps:

1. Give each person one full cask, one half-full cask, and one empty cask. This ensures that each person has an equal number of casks.

2. Now, let's distribute the remaining 4 full casks, 4 half-full casks, and 4 empty casks among the three people. Since 4 cannot be divided equally between 3 people, the remaining casks cannot be distributed equally.

3. Therefore, there is only one way to accomplish an equitable division in this scenario, which is to have each person receive one extra full, one extra half-full, and one extra empty cask.

The final distribution will be as follows:

Person 1: 2 full casks, 2 half-full casks, and 2 empty casks.

Person 2: 2 full casks, 2 half-full casks, and 2 empty casks.

Person 3: 2 full casks, 2 half-full casks, and 2 empty casks.

In this division, each person receives the same amount of wine (3 casks) and the same total number of casks (6 casks).

Please note that if there were a different number of casks or a different distribution of full, half-full, and empty casks, there might be additional ways to accomplish an equitable division.