23 prisoners. Two switches. The prisoners have to agree a strategy so that they know when all 23 prisoners have been in the switch room. One prisoner is The Counter. He counts the other prisoners. He uses the left switch as a counter. The idea is that each prisoner moves the left switch on once only, and only The Counter turns it off. On all other visits, all the prisoners switch the right switch. So he'd know exactly how many prisoners had seen the switch room. But there is a problem: how to start? On The Counter's first visit how does he know if the switch is on because it started on, or because it was switched by another prisoner. So they modify the rules so that each prisoner moves the left switch on twice only. Now The Counter is counting to 44. The first time the switch was on, it may not have been switched by one of the prisoners. But the next 43 times must each have been switched by a real prisoner, 42 of those were 21 prisoners switching twice, and the 43rd was the 22nd prisoner, who may have switched once or twice. This is not my solution, I came up with a probablistic solution which would have meant the prisoners could never be 100% *sure*. 1000 bottles problem. 1 bottle is poisoned. Which one? You have ten condemned prisoners who you can make drink the wine. You only have 24 hours, and it takes 24 hours for the poison to work. How do you find which bottle is poisoned. Label the first bottle 0000000001. The next is 0000000010. Continue like this *in binary*. Now the first prisoner drinks some wine if the first bit is 1, the second if the second is 1. All prisoners get very drunk. After 24 hours, the dead prisoners spell out the number of the poisoned bottle in binary! Dragon puzzle. seven wells on an island. Each is poison, but can be cured by a higher number. Only dragon can get to the top well. Knight and Dragon give each other a glass of water. Knight lives, Dragon dies. How? I worked out half the answer: the knight drinks from well 1 before hand, then he drinks the dragon's water, which is either more 1 and he's in trouble, or its a higher number and he's cured. then he drinks from 1 again. so whatever happens now he needs curing with a higher number than 1. Which is 2. But the other way around I couldn't see how he could be sure of getting the dragon. Turns out when I look it up, the puzzle is stated wrong. It's supposed to be an island IN A LAKE. He gives the dragon lake water, and the dragon thinking he's poisoned, kills himself with water from well 7. Gold bar puzzle. You must give your worker 1/7th of a gold bar per day for seven days, but you must only cut your gold bar twice. The way it is stated on the given page you have to give a total of one piece a day. That would be impossible, but The actual soltuion from the web is: You cut your gold bar into 1/7 2/7 and 4/7 pieces and use them like coins. On the first day you pay 1/7. On the second day you pay an additional 2/7 and demand 1/7 change! Pill puzzle. You have 5 jars of pills. Each pill weighs 10 gram, except for contaminated pills contained in one jar, where each pill weighs 9 gm. Given a scale, how could you tell which jar had the contaminated pills in just one measurement? My own solution: assuming there are at least five pills in each jar, put 1 pill from jar one, 2 pills from jar two, up to 5 from jar 5. These should weigh 150 grams in all. The deficit in grams is the number of the faulty jar.