Alright here is a solution.. Rock solid, but it will take awhile...
First, assign every kid a number and make sure they know thier number.. between 1 and 10.
- child1 is assigned to any day ending in 1. (Includes 1, 11, 21, 31 ...)
- subsequently all other children are assigned the days ending in thier number child2 gets 2, 12, 22 etc etc
- card starts black
- If child1 comes in on any day ending in 1, he flips the card from black to white
- If child2 comes in on his assigned day and sees the card white, he knows that child1 has been in the room the day before
- If any child enters the room on a day that they are not assigned to, and the card is white, they flip the card to black or leave it black
- Any child except for child1 who enters the room on thier assigned day and sees the card black, they leave it black
- Until such time as they come in and see the card is white on thier assigned day, from that point on they leave the card white, or flip it white on any assigned day after that...
- so... for example (days are arbitrary)
day 31 - child1 comes in and flips it white
32 - child2 comes in sees that it is white, now knows that child1 has been in the room and from then on will ensure they leave the card white or flips the card white on any day that ends in 2
..
..
..
as an example:
day 72 - child2, knowing for the last few months that child1 has visited the room, leaves the card white, or flips it white
day 73 - child3 sees the card white and knows from now on that both child1 and child2 have been in the room and from that point on leaves the card white or flips the card white on any of his assigned days.. Before this point, child3, not having proof of child 2 and 1, would have been leaving the card black or flipping to black..
so.. fast forward to day 2000 child10 enters the room. (he's pissed, his parents have abandoned him to the evil dictators of the math camp) sees the card white.. he knows that child9 was in the day before, and has proof that all other children have visited the room.. He then shoves the card down the counsellors throat and sues his parents..
BUT.. he gets to go home..
How's that Knifemissile?
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"Life is possible only with illusions. And so, the question for the science of mental health must become an absolutely new and revolutionary one, yet one that reflects the essence of the human condition: On what level of illusion does one live?"
-- Ernest Becker, The Denial of Death
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