1.There are 4 men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower mans pace.
1 and 2 cross together. 1 comes back. then 3 and 4 cross. 2 comes back. then 1 and 2 cross. Total time is 2+1+10+2+2 = 17.
2.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?
Take one pill from first, two from second, three from third and so on. Total pills are n(n+1)/2 and should weigh 10n(n+1)/2. If it weighs x gm less than that then the x'th jar is contaminated, since we took x pills from that jar which weighed 1 gm less.
3.One train leaves Los Angeles at 15 MPH heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
If distance is X miles between NY and LA, then it takes X/(15+20) hours for the trains to collide, and bird will have travelled 25X/(15+20) = 5X/7 miles in that time
4.Imagine that you have 26 constants, labelled A through Z. Each constant is assigned a value in the following way: A = 1; the rest of the values equal their position in the alphabet (B corresponds to the second position so it equals 2, C = 3, etc.) raised to the power of the preceeding constant value. So, B = 2 ^ (A's value), or B = 2^1 = 2. C = 3^2 = 9. D = 4^9, etc., etc. Find the exact numerical value to the following equation:
Answer is 0, because (X-X) is present in the product.
5.You have 12 balls. All of them are identical except one, which is either heavier or lighter than the rest - it is either hollow while the rest are solid, or solid while the rest are hollow. You have a simple two-armed scale, and are permitted three weighings. Can you identify the odd ball, and determine whether it is hollow or solid.
Let the balls be numbered 1 to 12. Firstly, put 1-4 on one side and 5-8 on other side. If both are equal then one of 9-12 is odd. Then second try, weigh 9-10 vs 1-2, if equal, one of 11-12 is bad, else 9-10 is bad. Testing which one is bad can be done by (third try) weighing 11 or 9, respectively, with good ball 1. It also gives whether the odd ball is heavy or light.
Man 1:1 minute to cross Man 2: 2 minutes to cross Man 3: 5 minutes to cross Man 4: 10 minutes to cross
1 and 2 cross together. 1 comes back. then 3 and 4 cross. 2 comes back. then 1 and 2 cross. Total time is 2+1+10+2+2 = 17.
2.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?
Take one pill from first, two from second, three from third and so on. Total pills are n(n+1)/2 and should weigh 10n(n+1)/2. If it weighs x gm less than that then the x'th jar is contaminated, since we took x pills from that jar which weighed 1 gm less.
3.One train leaves Los Angeles at 15 MPH heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
If distance is X miles between NY and LA, then it takes X/(15+20) hours for the trains to collide, and bird will have travelled 25X/(15+20) = 5X/7 miles in that time
4.Imagine that you have 26 constants, labelled A through Z. Each constant is assigned a value in the following way: A = 1; the rest of the values equal their position in the alphabet (B corresponds to the second position so it equals 2, C = 3, etc.) raised to the power of the preceeding constant value. So, B = 2 ^ (A's value), or B = 2^1 = 2. C = 3^2 = 9. D = 4^9, etc., etc. Find the exact numerical value to the following equation:
(X - A) * (X - B) * (X - C) * ... * (X - Y) * (X - Z)
Answer is 0, because (X-X) is present in the product.
5.You have 12 balls. All of them are identical except one, which is either heavier or lighter than the rest - it is either hollow while the rest are solid, or solid while the rest are hollow. You have a simple two-armed scale, and are permitted three weighings. Can you identify the odd ball, and determine whether it is hollow or solid.
Let the balls be numbered 1 to 12. Firstly, put 1-4 on one side and 5-8 on other side. If both are equal then one of 9-12 is odd. Then second try, weigh 9-10 vs 1-2, if equal, one of 11-12 is bad, else 9-10 is bad. Testing which one is bad can be done by (third try) weighing 11 or 9, respectively, with good ball 1. It also gives whether the odd ball is heavy or light.
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