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        riddles >> easy >> More Chickens and Eggs
        
(Message started by: ThudanBlunder on Aug 7^th, 2007, 4:21pm)

Title: More Chickens and Eggs
Post by ThudanBlunder on Aug 7^th, 2007, 4:21pm

If a chicken and a half lay an egg and a half in a day and a half, what is the smallest integer number of chickens you need to ensure that an integer number of dozens will be laid in a week?

Title: Re: More Chickens and Eggs
Post by Grimbal on Aug 8^th, 2007, 3:12am

Hm... can you combine partial eggs from 2 chicken at the end of the week? If a chicken lays 1 egg in 2 days, do 2 chicken lay 7 eggs every week, or 6 eggs the first week (with 2 eggs in process) and 8 the next week?

If the rate is an average (or by carefully starting the biological clock of the chicken with slight offsets), I get:
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3/2 chicks lay 3/2 eggs in 3/2 days.
1 chick lays 1 egg in 3/2 days.
1 chick lays 2 eggs in 3 days.
What about a week?
1 chick lays 2·7/3 eggs in 3·7/3 = 7 days.
You want a multiple of 12. Cancel denominator 3 and add a factor 6
18 chicks lay 2·7·6 eggs in 7 days.
18 chicks lay 7 dozen eggs in 7 days.

To actually get full dozens every week, let 6 chicken start on Monday morning, 6 other on Monday afternoon and the last 6 on Tuesday morning. The first team will complete the job on Tuesday afternoon and restart a new cycle. This way, you get 6 eggs every morning and 6 every afternoon. You get exactly 1 dozen every day. Except for the bootstrap period.

This does not take care of week-ends, and holidays (like Christmas and ... Easter).
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Title: Re: More Chickens and Eggs
Post by towr on Aug 8^th, 2007, 3:46am

[hide]How about 0?[/hide] :P