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Brain Teasers
Sharpen Your Mind
Every week 3 hard brain teasers will be posted up. Brain teasers are a great way to test logical reasoning and improve comprehension skills. The solution to these brain teasers will be posted the following week.
Easy
A certain bacteria population doubles every minute. At 11:00 am a small amount is placed in a container and at 12:00 am the container fills up. At what time was the container half full?
Previous Weeks
Gary, who can not read, write or spell, has just received a letter from his wife which he must answer at once. Of his three friends, Arnold is deaf, Bob is blind and Charlie can not speak. They can all read and write but the blind man only knows braille. Both the deaf man and the blind man are able to speak.
With the help of which two friends will the man be able to answer the letter?
Solution: Gary needs two tasks to be done for him:
1. Someone to read him the letter- the only person who can do this in one step is Arnold the deaf man (Bob can not see the letter therefore can not read it to him and Charlie can not read it to him because he is mute)
2.Someone to listen to what he wants to write an write it- the only person who can do this in one step is Charlie, the mute (Although Bob can listen, he only knows braille)
Therefore the two friends Gary requires is Arnold and Charlie
You’re standing in a hallway with three light switches on the wall, each of which turns on a different lamp inside a closed room. You can’t see inside the room, and you can’t open the door except to enter the room. You can enter the room only once, and when you do.
How can you tell which switch turns on which lamp by checking into the room only once?
Solution: Leave one of the switch's on for around a minute, then switch it off. Leave another switch on, then walk into the room. The bulb that was warm was from switch that was left on and turned off, the light which is still on corresponds to the switch that is left on. The cold bulb corresponds to the switch that was never turned on.
Gary, who can not read, write or spell, has just received a letter from his wife which he must answer at once. Of his three friends, Arnold is deaf, Bob is blind and Charlie can not speak. They can all read and write but the blind man only knows braille. Both the deaf man and the blind man are able to speak.
With the help of which two friends will the man be able to answer the letter?
Solution: Gary needs two tasks to be done for him:
1. Someone to read him the letter- the only person who can do this in one step is Arnold the deaf man (Bob can not see the letter therefore can not read it to him and Charlie can not read it to him because he is mute)
2.Someone to listen to what he wants to write an write it- the only person who can do this in one step is Charlie, the mute (Although Bob can listen, he only knows braille)
Therefore the two friends Gary requires is Arnold and Charlie
You’re standing in a hallway with three light switches on the wall, each of which turns on a different lamp inside a closed room. You can’t see inside the room, and you can’t open the door except to enter the room. You can enter the room only once, and when you do.
How can you tell which switch turns on which lamp by checking into the room only once?
Solution: Leave one of the switch's on for around a minute, then switch it off. Leave another switch on, then walk into the room. The bulb that was warm was from switch that was left on and turned off, the light which is still on corresponds to the switch that is left on. The cold bulb corresponds to the switch that was never turned on.
Medium
Two couples are sitting on a bench that can fit four people. What are the total number of arrangements given that each couple can not be separated?
At a family get-together there was a: Son, Daughter, Mother, Father, Aunt, Uncle, Niece, Nephew, and Cousin.
What is the fewest number of people present in the room?
Solution: The minimum number of people present in the room is four; A man and his son, The man's sister and her daughter.
In a medication research center, there are four canisters A,B, C and D standing side by side in that order. Each canister only contains one type of medication. There is a canister for influenza medication, which is next to the canister of gastro medication. There is a canister of antibiotics, which is next to the canister of influenza medication and a canister of headache medication.
Which canisters A,B,C and/or D can not have the headache medication?
Solution: Starting with the last statement, the antibiotic is next to both the canister of influenza medication and headache medication. This means it must be in position B or C (first assume that it is in B). From the first statement, influenza is next to gastro medication, therefore it can not be in position A and must be in position C. This results in the following order: A(headache), B(anti-biotics), C(influenza), D(gastro). Remember, the anti-biotics can also go in canister C. In this case the whole order is reversed A(gastro), B(influenza), C(anti-biotics), D(headache). Therefore the headache medication can not be in canister B or C.
Hard
Jerry has a bucket full of counters labelled from 100 to 999. Without looking inside, he must continue to draw counters until they have at least one digit in common. What is the maximum number of counters he must draw?
Previous Weeks
You have 10 bags with 10 gold coins each. Nine bags have genuine coins that weigh 10g each, but one bag has fake coins that are only 9g each.
Using a digital scale and only one weighing, how do you figure out which bag has the fake coins?
Solution: Label the bags from 1 to 10. From the the 1st bag, take out one coin. From the 2nd bag take out two coins. From the 3rd bag, take out three coins ... From the 10th bag take out 10 coins. Place all the coins on the digital scale and record the reading. If all the coins were genuine, the total sum of the mass would be:
10 + 2x10 + 3x10 + ... 10x10 =550g
The difference between the number of grams shown on the scale will specify which bag the fake coins are in. For example, if the reading shown 543 gram, it means that we are 7g short of all the coins being real. This must mean that 7 of the coins were not genuine. Since the fake coins are all in one bag (did not come from different bags), it must have come out from the one which we took out 7 coins (i.e. the 7th bag)
Albert and Bernard just became friends with Cheryl and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
May 15 ,May 16 ,May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
Cheryl then tells Albert and Bernard the month and days of her birthday respectively:
Albert: I don't know when Cheryl's birthday is, but I know Bernard does not know too
Bernard: At first I didn't know when Cheryl's birthday is but now I know.
Albert: Then I also know when Cheryl's birthday is.
When is Cheryl's birthday?
Solution: The two things to initially note is:
-Albert knows only the month: May,June, July, August
-Bernard knows only the day: 14 ,15 ,16 ,17 ,18 .19
Now review each statement:
Albert: I don't know when Cheryl's birthday is, but I know Bernard does not know too
Albert is sure that Bernard doesn't know as well, meaning all the days in the month that Albert is told, have another day with a repeated number. This means that the birthday is not in May (May 19th is unique, therefore if Bernard was told the number 19, he would instantly know the birthday. This is contradictory to the statement). By the same logic, the birthday is not in June (18 is unique in June 18th).
Bernard: At first I didn't know when Cheryl's birthday is but now I know.
The fact that Bernard knows now, means that his number is unique to July and August (May and June have already been cancelled). Therefore the possible dates are July 16, August 15 and August 17 (we can remove August and July 14 because the day is present in both July and August. This means that if it was Bernard was told the day 14, he still wouldn't know the date)
Albert: Then I also know when Cheryl's birthday is.
The fact that Albert knows now means that from the month given, there is only one option left. This is true only for July 16. If it was in August, he would still not know the date as there are two option; August 15 and August 17, still remaining.
Therefore Cheryl's birthday is on July 16th
You have 10 bags with 10 gold coins each. Nine bags have genuine coins that weigh 10g each, but one bag has fake coins that are only 9g each.
Using a digital scale and only one weighing, how do you figure out which bag has the fake coins?
Solution: Label the bags from 1 to 10. From the the 1st bag, take out one coin. From the 2nd bag take out two coins. From the 3rd bag, take out three coins ... From the 10th bag take out 10 coins. Place all the coins on the digital scale and record the reading. If all the coins were genuine, the total sum of the mass would be:
10 + 2x10 + 3x10 + ... 10x10 =550g
The difference between the number of grams shown on the scale will specify which bag the fake coins are in. For example, if the reading shown 543 gram, it means that we are 7g short of all the coins being real. This must mean that 7 of the coins were not genuine. Since the fake coins are all in one bag (did not come from different bags), it must have come out from the one which we took out 7 coins (i.e. the 7th bag)
Albert and Bernard just became friends with Cheryl and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
May 15 ,May 16 ,May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
Cheryl then tells Albert and Bernard the month and days of her birthday respectively:
Albert: I don't know when Cheryl's birthday is, but I know Bernard does not know too
Bernard: At first I didn't know when Cheryl's birthday is but now I know.
Albert: Then I also know when Cheryl's birthday is.
When is Cheryl's birthday?
Solution: The two things to initially note is:
-Albert knows only the month: May,June, July, August
-Bernard knows only the day: 14 ,15 ,16 ,17 ,18 .19
Now review each statement:
Albert: I don't know when Cheryl's birthday is, but I know Bernard does not know too
Albert is sure that Bernard doesn't know as well, meaning all the days in the month that Albert is told, have another day with a repeated number. This means that the birthday is not in May (May 19th is unique, therefore if Bernard was told the number 19, he would instantly know the birthday. This is contradictory to the statement). By the same logic, the birthday is not in June (18 is unique in June 18th).
Bernard: At first I didn't know when Cheryl's birthday is but now I know.
The fact that Bernard knows now, means that his number is unique to July and August (May and June have already been cancelled). Therefore the possible dates are July 16, August 15 and August 17 (we can remove August and July 14 because the day is present in both July and August. This means that if it was Bernard was told the day 14, he still wouldn't know the date)
Albert: Then I also know when Cheryl's birthday is.
The fact that Albert knows now means that from the month given, there is only one option left. This is true only for July 16. If it was in August, he would still not know the date as there are two option; August 15 and August 17, still remaining.
Therefore Cheryl's birthday is on July 16th