Problem of the Week #4: Monday Jan. 30th, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems. Please refrain from posting full solutions.
This is based on a scenario Bradley Epp has shared via the BCAMT Discussion on Jan. 24th, 2023. Here’s a copy of the original message (shared with permission. Thank you Bradley):
Here’s one for everyone.
My colleague has 8 chickens – they have bands on their eggs (different colours).
3 are not laying eggs
1 sometimes lays eggs.
What is the best way to determine which chickens are laying eggs?
Get rid of the trivial answer…there are 8 chickens in 8 boxes…
And so…have fun?
Here are a few problems inspired by this scenario:
a). If every chicken lays an egg each day, and each chicken has an identifiable pattern of bands on its eggs, how many days does it take to match 8 chickens each to its egg pattern using two boxes?
b). How many days does it take using three boxes? Four?
c). What is the maximum number of chickens we can identify to their eggs in the number of days in a) using three boxes? Four?
d). Now in the 8 chickens we have, 3 are not laying eggs and 1 sometimes lays eggs. Without knowledge about the frequency the sometimes-egg-laying chicken lays eggs, devise a plan that would identify the sometimes-egg-laying chicken to its egg pattern in the shortest time possible using two boxes.
e). We have 8 chickens; 4 of which are not laying eggs, and the rest lay eggs each day. If all eggs are white and indistinguishable, how many days does it take to separate the three types of chickens from each other using two boxes?
f). Same as e)., but now with 3 non-laying chickens and 1 sometimes-laying chicken with unknown frequency of egg laying.
g). Share your problem inspired by this scenario.