Logic Development Problems

Puzzle #1 Smita has a full 8-quart container (Container A) of peanut oil. She wants to share half of the oil with her sister. She has another 2 empty containers (B and C) with the capacities: 5 quarts and 3 quarts. Can you, without weighing the containers, put 4 quarts of oil in container B with the least number of steps for her sister?

SolutionPuzzle # Initially Step Step2323 Step Step4152 Step 5143

Puzzle #2 On the right, you see a silver and a golden pot. One of these pots contains a treasure and the other one is empty. Assume that you can determine from the text prints which pot contains the treasure. The text prints on the pots are: The silver pot: "This pot is empty." The golden pot: "Exactly one of these texts is true." The Question: Which pot contains the treasure?

Solution Puzzle #2 Assume that the print on the first (silver) pot is right. Assume also the second print (on the golden pot) to be right. So now we assume that both prints hold, but this means that only one print holds (according to the second print). This leads to a contradiction!

Solution Puzzle #2 So the assumption that the second print holds is wrong! This means that the second print does not hold. So now we assume that only the first print holds, but this would make the second print right. Which again leads to a contradiction!

Solution Puzzle #2 So the assumption that the first print holds is wrong! This means that the first print does not hold. (We can also prove that the correctness of the second print is of no concern anymore.) Conclusion: The silver pot contains the treasure!...

Puzzle #3 Take out 9 matches to make all squares disappear

Solution Puzzle #3

Puzzle #4 In a dark forest lives a population of 400 highly intelligent people. All people look exactly alike, but only differ in the fact that they are wearing either a red or a blue hat. There are 250 people with a red hat and 150 people with a blue hat. Interestingly, they themselves don't know these numbers themselves and that none of them knows what the colour of his hat is. But the people do know that there is at least one of them with a red hat. After some time, there is a big party in this village, to which initially all people will go. However, this party is only intended for those wearing a blue hat. Those with a red hat are supposed never to return to the party again, as soon as they know that they are wearing a red hat. You have to tell that how many days does it take before there are no more people with red hat that are left at party?

Solution Puzzle #4 The answer is: after 250 days there are no people with red hats left at the party.

Solution Puzzle #4 Let us consider the situation where there is only 1 person with a red hat. In that case, this person would arrive at the party on the first day, and notice that he doesn't see any red hats. Since he knows that there should be at least 1 person with a red hat, he concludes that he must have a red hat himself. As a consequence, the next day he doesn't show up at the party anymore.

Solution Puzzle #4 If there would be two peoples with red hats, they both would see each other with a red hat on the first day. They know that if this person doesn't return on the next day, he must have been the only one. If he returns, then there is no other conclusion then that they both must have a red hat. As a consequence, after 2 days they don't return to the party.

Solution Puzzle #4 Since there are 250 red hats is identical, only now it takes 250 days before all peoples with red hats can conclude that they must have a red hat.

Puzzle #5 Here are three answers: –Answer A –Answer A or B –Answer B or C The Question: There is only one correct answer to this question. Which answer is this?

Solution Puzzle #5 If answer A would be correct, then answer B ("Answer A or B") would also be correct. If answer B would be correct, then answer C ("Answer B or C") would also be correct. This leads to the conclusion that if either answer A or answer B would be the correct answer, there are at least two correct answers.

Solution Puzzle #5 This contradicts with the statement that "there is only one correct answer to this question". If answer C would be correct, then there are no contradictions. So the solution is: answer C.