An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advice. After hearing the advice they jump on the camels and race as fast as they can to the city.
What does the wise man say?
Solution:
Gur jvfr zna gbyq gurz gb fjvgpu pnzryf.
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Thursday, September 18, 2008
The 3 Bulbs Problem
Imagine you are in a room with 3 switches. In an adjacent room there are 3 bulbs (all are off at the moment), each switch belongs to one bulb. It is impossible to see from one room to another. How can you find out which switch belongs to which bulb, if you may enter the room with the bulbs only once?
The Witch Game
There are a group of 10 people travelling on a certain journey. On the way they come across a dense forest which they need to cross. After a lot of consideration they finally decide to go on the move. But unfortunately on the way they get trapped by a witch, who gets them all tied-up and bound. Now they try to please the witch in every way possible to save their skin.
Finally the witch agrees to a certain condition. Here goes the condition:
The witch had an infinite number of red and blue caps with her. So she decides to get them standing in a row, facing the same direction and placing a cap on each of their head (the cap could be of any color either blue or red). Now each of them has to guess the color of the cap on their head starting from the guy standing at the end of the row. If he is right he would be spared of his life else he would be killed by the witch. The only saving grace was, they were given a chance to decide a strategy which would enable the maximum number of the group to save their lives.
What do you think the optimum strategy should be which could save the maximum number of them and how many will that be?
Note: You can assume the group functions as a whole and each one has an altruistic behavior wherein they think of the benefit of the whole group rather than their own.
You can also assume, what one person speaks is audible to the rest of the group.
Each of the men are given only a single chance to guess the color of the cap on his head.
They are not supposed to do anything else other than just speak out the color - 'just one word'.
Finally the witch agrees to a certain condition. Here goes the condition:
The witch had an infinite number of red and blue caps with her. So she decides to get them standing in a row, facing the same direction and placing a cap on each of their head (the cap could be of any color either blue or red). Now each of them has to guess the color of the cap on their head starting from the guy standing at the end of the row. If he is right he would be spared of his life else he would be killed by the witch. The only saving grace was, they were given a chance to decide a strategy which would enable the maximum number of the group to save their lives.
What do you think the optimum strategy should be which could save the maximum number of them and how many will that be?
Note: You can assume the group functions as a whole and each one has an altruistic behavior wherein they think of the benefit of the whole group rather than their own.
You can also assume, what one person speaks is audible to the rest of the group.
Each of the men are given only a single chance to guess the color of the cap on his head.
They are not supposed to do anything else other than just speak out the color - 'just one word'.
The 50 bulbs problem
Prime Minister of Einsteinia lost the Mensa annual challenge and committed suicide.The King of Einsteinia had some doubts on the abilities of the Deputy Prime Minister. The King devised a plan to test his intelligence before promoting him.
He put 50 light bulbs in a room and put the corresponding 50 switches in another room. He switched on "x" number of these bulbs. He told the Deputy Prime Minister the number of bulbs that are switched on (x) and gave him the task of dividing the fifty switches into two groups such that each group had equal number of lit bulbs. The Deputy Prime Minister was allowed to go to the room with the bulbs or to the room with the switches but could not see one room from the other. By looking at the switch there is no way to tell whether the corresponding bulb is on or off. Flipping the switch each time toggles the state of the corresponding bulb.
Can you help the Deputy Prime Minister in devising a strategy?
Solution:
Ba cbfvgvba - Gur ohyo gb juvpu gur fjvgpu orybatf gb vf BA (abg gur culfvpny cbfvgvba bs gur fjvgpu)
Yrgf fnl gur QCZ pubbfrf nal 'k' fjvgpurf bhg bs gur 50.
Abj, vs 'a' fjvgpurf bhg bs guvf 'k' ner va gur BA cbfvgvba gur erfg bs gur 'k-a' fjvgpurf juvpu ner nyfb BA orybat gb gur bgure tebhc bs '50 - k' fjvgpurf.
Fb, abj vs gur QCZ gbttyrf gur cbfvgvba bs nyy gur 'k' fjvgpurf gung ur fryrpgrq, 'a-k' fjvgpurf jbhyq abj or va gur BA cbfvgvba. Guvf vf fnzr nf gur ahzore bs fjvgpurf va gur BA cbfvgvba va gur bgure tebhc.
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He put 50 light bulbs in a room and put the corresponding 50 switches in another room. He switched on "x" number of these bulbs. He told the Deputy Prime Minister the number of bulbs that are switched on (x) and gave him the task of dividing the fifty switches into two groups such that each group had equal number of lit bulbs. The Deputy Prime Minister was allowed to go to the room with the bulbs or to the room with the switches but could not see one room from the other. By looking at the switch there is no way to tell whether the corresponding bulb is on or off. Flipping the switch each time toggles the state of the corresponding bulb.
Can you help the Deputy Prime Minister in devising a strategy?
Solution:
Ba cbfvgvba - Gur ohyo gb juvpu gur fjvgpu orybatf gb vf BA (abg gur culfvpny cbfvgvba bs gur fjvgpu)
Yrgf fnl gur QCZ pubbfrf nal 'k' fjvgpurf bhg bs gur 50.
Abj, vs 'a' fjvgpurf bhg bs guvf 'k' ner va gur BA cbfvgvba gur erfg bs gur 'k-a' fjvgpurf juvpu ner nyfb BA orybat gb gur bgure tebhc bs '50 - k' fjvgpurf.
Fb, abj vs gur QCZ gbttyrf gur cbfvgvba bs nyy gur 'k' fjvgpurf gung ur fryrpgrq, 'a-k' fjvgpurf jbhyq abj or va gur BA cbfvgvba. Guvf vf fnzr nf gur ahzore bs fjvgpurf va gur BA cbfvgvba va gur bgure tebhc.
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