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Monthly Archives for February, 2013



Summing products

Posted on: February 28th, 2013 by
2

Consider nonempty subsets of the set {1,2,...,N}. For each such subset we can compute the product of the reciprocals of each member. Find the sum of all such products. via Australian Mathematical Society gazette puzzle corner

Weight of a Juggler

Posted on: February 27th, 2013 by
16

What is the weight of a juggler? Clarification: If the juggler of weight W stands on a weighing machine and juggles n balls, each of weight w, what does the weighing machine read? Assume the juggler is fast enough that the weighing machine's reading is the average weight it measures. -- Via Tom Cover.

Flying with limited fuel

Posted on: February 26th, 2013 by
Comments Requested

There is an airport with virtually infinite fuel and infinite planes. However, each airplane can only hold fuel for up to 1000 miles. You want to send an airplane across a desert that is 10000 miles long. You can deploy additional airplanes and have airplanes exchange fuel along the way. However, you DO NOT WANT any airplane to be stranded in the middle of the Continue reading the story "Flying with limited fuel"

The blue-eyed islanders puzzle – repost

Posted on: February 25th, 2013 by
3

There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). Continue reading the story "The blue-eyed islanders puzzle – repost"

Letter puzzle

Posted on: February 25th, 2013 by
1

Why are some letters above the red line and some letters below?   via Cool Math 4 Kids - Brain Benders

Apples delivery

Posted on: February 23rd, 2013 by
16

The distance between the towns A and B is 1000 miles. There is 3000 apples in A, and the apples have to be delivered to B. The available car can take 1000 apples at most. The car driver has developed an addiction to apples: when he has apples aboard he eats 1 apple with each mile made. Figure out the strategy that yields the largest Continue reading the story "Apples delivery"

Cross a bridge

Posted on: February 23rd, 2013 by
2

A group of four people has to cross a bridge. It is dark, and they have to light the path with a flashlight. No more than two people can cross the bridge simultaneously, and the group has only one flashlight. It takes different time for the people in the group to cross the bridge: Annie crosses the bridge in 1 minute, Bob crosses the bridge in 2 Continue reading the story "Cross a bridge"

Next term in sequence:

Posted on: February 23rd, 2013 by
2

What is the next term in the following sequence? O, T, T, F, F, S, S, E, ... For hint: View comments.

Sherlock Holmes

Posted on: February 18th, 2013 by
1

Sherlock Holmes and Dr Watson were going camping. They pitched their tent under the stars and went to sleep. Sometime in the middle of the night Holmes woke Watson up and said: "Watson, look up at the sky, and tell me what you see." Watson replied: "I see millions and millions of stars." Holmes said: "And what do you deduce from that?" Watson replied: "Well, Continue reading the story "Sherlock Holmes"

Two bulbs vs one bulb

Posted on: February 14th, 2013 by
Comments Requested

Suppose the life-time of a light bulb of type A is an exponential RV with mean 1 month, and that of type B is exponential with mean 2 months. Is it better to have 2 bulbs of type A or 1 bulb of type B? Come up with the answer without doing the math.

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