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Monthly Archives for November, 2013

Jealous husbands problem

Posted on: November 30th, 2013 by

3 men and their wives (6 people in total) want to cross a river in a boat that can hold at most 2 people. No woman can be in the same side as another man unless her husband is present. Show how all 6 people can cross the river. - via Wikipedia

Another river crossing puzzle

Posted on: November 29th, 2013 by
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3 men and 3 monsters want to cross the river. They have a boat that can carry at most 2 people at a time. If there are more monsters than men on either side of the river, all men on the outnumbered side will be eaten. Show how you can transport all 6 people across the river without having any man be eaten by the Continue reading the story "Another river crossing puzzle"

A River crossing puzzle

Posted on: November 28th, 2013 by

There are 2 small bots and 2 big bots. They have a boat to take them across the river. The boat can carry either 2 small bots or 1 big bot. At least 1 bot must ride the boat. Show how all 4 bots can cross the river. Try playing the game at Transum

Distance, time and speed

Posted on: November 27th, 2013 by

A, B and C run a 100 meters race. A beats B by 20 meters, and B beats C by 20 meters. By how much does A beat C? Assume A,B and C all run at constant speeds v_A, v_B, v_C respectively. - via Gpuzzles

Count F

Posted on: November 26th, 2013 by

How many occurrences of the letter 'F' can you find in the sentence below: "FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS" - via GPuzzles

Find your way

Posted on: November 25th, 2013 by

You have a road network where all intersections are 3-way intersections. You are trying to find a restaurant that's located at a particular intersection. However, all intersections are identical (except the one with the restaurant). Also, you are not allowed to mark anything on the roads. How will you find your way to the restaurant? - via Math Exchange

Points in a rectangle

Posted on: November 24th, 2013 by

If you choose 6 points inside a rectangle of dimensions 3cm x 4cm, show that the distance between some two of these 6 points is less than \sqrt{5}. - via Math puzzles

Lucky number

Posted on: November 23rd, 2013 by
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A 6-digit number is lucky if the sum of the first three digits equals the sum of the last three digits. Show that the sum of all 6-digit lucky numbers is divisible by 13. - via Math Puzzles

Missing dollar

Posted on: November 22nd, 2013 by

Three people eat at a hotel. The bill turned out to be $30. Each person paid $10. The clerk later finds that the bill is only $25. He sends an assistant to return the $5 to the 3 people. The assistant returns $1 to each of the 3 people and keeps $2 to himself. Now each person has effectively paid $9, thus a total of Continue reading the story "Missing dollar"

An online learning game

Posted on: November 21st, 2013 by
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Suppose X_1(t),X_2(t),\dots X_n(t) are input bits (i.e. 0 or 1) at time t, and Y(t) is the output bit. You are given samples for t=1,2,3,4,\dots. You know that Y(t) is the OR (or disjunction) of a subset of X_1(t),X_2(t),\dots X_n(t). For example Y=X_1 OR X_n, Y=X_3 OR X_5 OR X_6. You want to use online learning to learn the function that maps the inputs $$X_1,\dots Continue reading the story "An online learning game"

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