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Easy Deduction
A teacher thinks of two consecutive numbers between 1 and 10. The first student knows one number and the second student knows the second number. The following exchange takes place:
First: I do not know your number.
Second: Neither do I know your number.
First: Now I know.
What are the 4 solutions of this easy number puzzle?Answer
None of the students can have numbers 1 or 10, since they would guess the other one’s number with no problems.
I will describe solutions at one end of the interval of numbers 1-10 (the same can be done on the other end).
Information that the second student does not know must be important for the first student.So the first one must expect that the second one has 1 or 3 (if the first one has 2).
And as the second student does not know, then he has certainly not 1.
So the first pair is 2 and 3.
If the first one had 3, then he would expect the other one to have either 2 or 4.
But if the second one had 2 (and the second one would have known that the first one does not have 1), then he would know the number of the first student.
However, neither the second student knows the answer – so he has 4.
The second pair of numbers is 3 and 4.
Solutions at the other end of interval are 9 and 8 or 8 and 7.
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Birthday
The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year.
What day is my birthday?Answer
He was born on December 31st and spoke about it on January 1st.
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Water bowls 2
Given three bowls: 8, 5 and 3 liters capacity, divide 8 liters in half (4 + 4 liters) with the minimum number of water transfers. Note that the 8-liter bowl is initially filled with 8 liters of water and the other two bowls are empty – that is all water you have.
Answer
- Pour 5 litres from the 8-litre to the 5-litre bowl,
- Pour 3 litres from the 5-litre to the 3-litre bowl,
- Pour these 3 litres back to the 8-litre bowl,
- Pour the remaining 2 litres from the 5-litre to the 3-litre bowl,
- Pour 5 litres from the 8-litre to the 5-litre bowl,
- Pour the missing 1 litre from the 5-litre to the 3-litre bowl (there should be 4 litres left in the 5-litre bowl),
- Pour the 3 litres back from the 3-litre to the 8-litre bowl (and that’s it – in 8-litre bowl 4 litres).
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Water bowls 1
If you had a 5-liter bowl and a 3-liter bowl, and an unlimited access to water, how would you measure exactly 4 liters?
Answer
Fill the 5-litre bowl and pour water to the 3-litre bowl, which you empty afterwards. From the 5-litre bowl pour the 2 remaining litres to the 3-litre bowl. Refill the 5-litre bowl and fill in the 3-litre bowl (with 1 litre), so there stay the 4 required litres in the 5-litre bowl.
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Cannibals and Missionaries
Three missionaries and three cannibals want to get to the other side of a river. There is a small boat, which can fit only two. To prevent a tragedy, there can never be more cannibals than missionaries together.
Answer
1 cannibal and 1 missionary there, missionary back. 2 cannibals there, 1 cannibal back. 2 missionaries there, 1 missionary and 1 cannibal back. 2 missionaries there, 1 cannibal back. This one cannibal takes the remaining cannibals to the other side.
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She-goat, Wolf and Cabbage
A farmer returns from the market, where he bought a she-goat, a cabbage and a wolf. On the way home he must cross a river. His boat is small and won’t fit more than one of his purchases. He cannot leave the she-goat alone with the cabbage (because the she-goat would eat it), nor he can leave the she-goat alone with the wolf (because the she-goat would be eaten).
How can the farmer get everything on the other side of the river?Answer
Take the she-goat to the other side. Go back, take cabbage, unload it on the other side where you load the she-goat, go back and unload it. Take the wolf to the other side where you unload it. Go back for the she-goat. That’s it.