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rsl12 · 03-20-2004, 03:51 AM

I assume you can't choose to put the card on different spots on the table or write anything on it or chip it or rotate it...

this is an interesting problem too. This is the best solution I could think of so far:

Before anyone starts, the card shows black. It's decided that, for the first 9 days, the only person who wil flip the card to white will be the first person to go to the room twice. If no-one goes to the room twice in 9 days, then the 9th person, seeing the card is black, can immediately declare that it's everyone's been in the room. Otherwise, after 9 days, the 9 people can be divided into 4 groups: the ones that, the first time they came into the room, saw that the card was black; those that saw it was white the first time they came in; the person who flipped the card from black to white, and those who never got to the room in the 1st 9 days. The person who flipped the card will be the one who collects information from the others. When he flips the card on Day X (i'll assume it's a boys camp), he knows that at least X-1 people (the people who saw black, including himself) will have entered the room by day 9. The people who saw black have nothing else to do--they've already been counted by the information gatherer. The other people (those who saw white or didn't enter the room at all) need to be counted now. Starting with the person who enters on Day 9, here's the procedure:

If those who haven't been counted see that the card is white, they flip it to black. Once they flip it one time, any subsequent time they enter the room they do nothing, no matter what they see.

Those who have been counted never do anything.

The information gatherer flips the card to white whenever he sees that it is black.

The information gatherer will count the number of times he sees the card is black after day 9. If he sees the card is black 9-(x-1) days, then he knows that everyone has been in the room!

But this is potentially a LONG procedure--if camp is only 3 months, I think you'd be lucky if you cut your time in camp by half. I will try to think of a better solution.

03-20-2004, 03:51 AM	#2 (permalink)
rsl12 On the lam Location: northern va	I assume you can't choose to put the card on different spots on the table or write anything on it or chip it or rotate it... this is an interesting problem too. This is the best solution I could think of so far: Before anyone starts, the card shows black. It's decided that, for the first 9 days, the only person who wil flip the card to white will be the first person to go to the room twice. If no-one goes to the room twice in 9 days, then the 9th person, seeing the card is black, can immediately declare that it's everyone's been in the room. Otherwise, after 9 days, the 9 people can be divided into 4 groups: the ones that, the first time they came into the room, saw that the card was black; those that saw it was white the first time they came in; the person who flipped the card from black to white, and those who never got to the room in the 1st 9 days. The person who flipped the card will be the one who collects information from the others. When he flips the card on Day X (i'll assume it's a boys camp), he knows that at least X-1 people (the people who saw black, including himself) will have entered the room by day 9. The people who saw black have nothing else to do--they've already been counted by the information gatherer. The other people (those who saw white or didn't enter the room at all) need to be counted now. Starting with the person who enters on Day 9, here's the procedure: If those who haven't been counted see that the card is white, they flip it to black. Once they flip it one time, any subsequent time they enter the room they do nothing, no matter what they see. Those who have been counted never do anything. The information gatherer flips the card to white whenever he sees that it is black. The information gatherer will count the number of times he sees the card is black after day 9. If he sees the card is black 9-(x-1) days, then he knows that everyone has been in the room! But this is potentially a LONG procedure--if camp is only 3 months, I think you'd be lucky if you cut your time in camp by half. I will try to think of a better solution. __________________ oh baby oh baby, i like gravy. Last edited by rsl12; 03-20-2004 at 03:56 AM..