Arrange Cows in Pens: 1000 Cows & 10 Pens

[keemosabi]

Given 1000 cows and 10 pens, you want to arrange the cows in the pens such that any number of cows from 1 to 1000 can be obtained by opening certain pens and taking all the cows in those pens. How do you arrange the cows in the pens?

 

[Yuqing]

This is equivalent to finding a binary representation for a number. Arrange the cows like this

1, 2, 4, 8, 16, 32, 64, 128, 256 and the remaining 489

If the given number is smaller than 489, then simply open the first 9 pens according to the binary representation of the number. If the number is larger then open the 489 pen, and open the remaining again in binary.

 

[HallsofIvy]

Did we just recently have this puzzle?

 

[Amergin]

Concerning the solution to the riddle. The use of the binary notation is interesting.When I was younger and we weighed in lbs and ozs we had a set of scales with weights that stacked neatly by the side of the scales The weights were 1,2,4,8 and 1 lb =16oz then the same with lb weights stopping at7lb , I think.
My mother could weigh any weight with these. Question. Was the 16 ounces =One pound deliberately chosen for the given reason or was it accidental??

 

[CellCoree]

I would approach this problem by considering the most efficient and practical way to arrange the cows in the pens. One possible solution could be to divide the 1000 cows into 10 groups of 100, and then assign each group to a different pen. This way, if we need to obtain a specific number of cows, we can simply open the corresponding pens and take all the cows in those pens.

Another approach could be to arrange the cows in a hierarchical manner, with larger pens containing smaller pens within them. For example, the first pen could contain 500 cows, the second pen could contain 250 cows, and so on, until the last pen contains only 1 cow. This way, we can easily obtain any number of cows by opening the appropriate combination of pens.

Additionally, we could also consider implementing a color-coding system for the cows and pens. This would make it easier to keep track of which cows are in which pens, and which pens need to be opened to obtain a specific number of cows.

Overall, the key to arranging the cows in the pens in a way that allows for easy retrieval of any number of cows is to have a clear and organized system in place. By carefully considering the logistics and implementing efficient strategies, we can ensure that the cows are arranged in a way that meets the given criteria.