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Association for Computing Machinery

FORK IN THE ROAD (FALL 2019)

Puzzle:

You are traveling down a country lane to a distant village. You reach a fork in the road and find a pair of identical twin sisters standing there.

  • One is standing on the road to village and the other is standing on the road to Neverland (of course, you don’t know or see where each road leads).
  • One of the sisters always tells the truth and the other always lies (of course, you don’t know who is lying).
  • Both sisters know where the roads go.

If you are allowed to ask only one question to one of the sisters to find the correct road to the village, what will your question be?

Solution:

This is one of the most famous logic problems which can be solved by using classic logic operations. You may have heard a few variations of this puzzle before (eg. 2 doors - 1 to heaven and 1 to hell) but still, it's one of the best brain teasers.

There are a few types of logic questions:

  1. Indirect question: "Hello there beauty, what would your sister say, if I asked her where this road leads?" The answer is always negated.
  2. Tricky question: "Excuse me lady, does a truth telling person stand on the road to the village?" The answer will be YES, if I am asking a truth teller who is standing at the road to village, or if I am asking a liar standing again on the same road. So I can go that way. A similar deduction can be made for negative answer.
  3. Complicated question: "Hey you, what would you say, if I asked you ...?" A truth teller is clear, but a liar should lie. However, she is forced by the question to lie two times and thus speak the truth.

(SOURCE: BrainDen)

 

THE BURNING ISLAND (SUMMER 2019)

Puzzle:

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the man survive the fire? (There are no buckets or any other means to put out the fire.)

Solution:

The man picks up a piece of wood and lights it from the fire on the west end of the island. He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area. The man survives the fire, but dies of starvation, with all the food in the forest burnt.

(SOURCE: Math Is Fun)

 

CENSUS TAKING (SPRING 2019)

Puzzle:

A census taker approaches a house and asks the woman who answers the door, “How many children do you
have, and what are their ages?”

The woman replies, “I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door.”


The census taker walks next door, comes back, and says, “I need more information.”

The woman replies, “I have to go, my oldest child is sleeping upstairs.”

The Census taker replies, “Thank you, I now have everything I need.”

What are the ages of each of the three children?

Solution:

The reason the census taker could not figure out the children's ages is because, even with knowing the number on the house next , there were still two possibilities.

The only way that the product could be 36 and still leave two possibilities is when the sum equals 13. These possibilities being 9, 2 and 2 and 6, 6 and 1.

When the home owner stated that her "oldest" child is sleeping she was giving ths census taker the fact that there is an "oldest".

So the children's ages are 9, 2 and 2.

(SOURCE: Math Is Fun)