A Corny Question

A merchant has 21 sacks of grain: 7 full, 7 half-full and 7 empty. He wants to divide them equally among his three sons. How can he do this, without transferring any grain between sacks, so each son has the same quantity of grain and number of sacks?

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We know each son must end up with 7 sacks and 3.5 sacks of grain, since (7 sacks + 7 half sacks) / 3 = 3.5 sacks each.
There are two solutions.Solution 1
Son 1: 3 full, 1 half-full and 3 empty.
Son 2: 3 full, 1 half-full and 3 empty.
Son 3: 1 full, 5 half-full and 1 empty.Solution 2
Son 1: 2 full, 3 half-full and 2 empty.
Son 2: 2 full, 3 half-full and 2 empty.
Son 3: 3 full, 1 half-full and 3 empty.

We know each son must end up with 7 sacks and 3.5 sacks of grain, since (7 sacks + 7 half sacks) / 3 = 3.5 sacks each.
There are two solutions.

Solution 1
Son 1: 3 full, 1 half-full and 3 empty.
Son 2: 3 full, 1 half-full and 3 empty.
Son 3: 1 full, 5 half-full and 1 empty.

Solution 2
Son 1: 2 full, 3 half-full and 2 empty.
Son 2: 2 full, 3 half-full and 2 empty.
Son 3: 3 full, 1 half-full and 3 empty.

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9 Comments on "A Corny Question"

CHIEDZA says
April 29, 2015 @ 13:49

He will just divide 7 full sacks in halves. and put each half in empty sacks, to make 21 half sacks in all. He will therefore give each son 7 half sacks

Dan says
April 29, 2015 @ 14:37

That would be transferring grain between sacks as the empty sacks would no longer be empty.

Chiedza Muswaka says
April 29, 2015 @ 18:54

Take 7 full sacks and 7 empty sacks. Divide the contents in each full sack in half and put half the contents in each empty sack to make 21 half empty sacks in all. Then divide 21 by 3 to give each son 7 half sacks each.

Dan says
April 30, 2015 @ 09:47

You seem to be missing the requirement that you must not “[transfer] any grain between sacks”.

Lynn says
October 17, 2015 @ 16:17

Each son gets 2 full 2 half full and 2 empty bags of grain

sean says
April 26, 2016 @ 13:36

The first son gets 3 full sacks, 1 half sack, and 3 empty sacks . The other 2 get 2 full sacks, 3 half sacks, and 2 empty sacks.

Gabby says
June 4, 2016 @ 23:40

Sell the grain and give them money. It was a dumb idea.

Sankalpa says
August 16, 2016 @ 00:48

First son gets 3 full sacks, a half empty sack and 3empty sacks, all total 7 sacks. The second and third sons get 2 empty sacks, 2 full sacks and 3 half empty sacks each, all total 14 sacks. And there you have it 21 sacks divided among 3 brothers.

Rambo says
May 17, 2019 @ 04:20

He burns all the grain, then each son gets the same amount: none.

A Corny Question

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