In a remote country, it was decided to increase the number of male population. The proposal was to allow each family to have as many children as they want but only one girl. In other words, as soon as a family had one girl they could have no more children. As long as they had all boys they could keep having children. Would this achieve the desired result of increasing the male population?
Answer:
Outwardly it may seem that the above system contains no flaw but however a deeper reflection will tell that it is nothing short of a fallacy. When all the families rear so much of boys and so few girls where is the question of procreation and proliferation of mankind? The world would become a galaxy of male species and disproportionate females so as to create an imbalance and comes to an dead end, a cul-de-sac.
72. DOOR TO FREEDOM
You have been knocked unconscious and kidnapped. You wake up in a bare and dungeon room that contains two identical doors, each guarded by a grim silent guard. A voice on a loudspeaker explains that one of these doors leads to freedom, the other to instant death. You are told that one of the guards will always tell the truth and the other will always lie, but you are not informed which guard is the liar. Nor you know which one speaks truth. You will be permitted to select a guard and ask him only one question that requires a yes or no answer. After receiving the answer to this one question, you must select a door and meet your fate. What question can you ask that will assure your freedom?
Answer:
Ask either guard, "If I asked the other guy if this door you are guarding is the door to freedom, would he say yes?" If you get a "no"answer, it is safe to use the door. Here's why: You might have talked to the LIAR guarding the door to FREEDOM. If so, you would get a "no" answer, since the other guard, the truth-teller, would say yes, so the liar you are talking to would say no. If you were talking to the TRUTH-TELLER guarding the door to FREEDOM, you would also get a "no" answer, since the other guard, the liar would say "no" and the guard you were talking to would truthfully report this to you. If you were talking to the LIAR guarding the door to DEATH, you would get a "yes" answer. If you were talking to the TRUTH-TELLER guarding the door to DEATH, you would also get a "yes" answer. There are no other possibilities.
73. GOING FARTHEST.
Four brothers have a horrible fight and decide to get away as far away from each other as humanly possible. Assuming they stay on the surface of the earth (of course) where should they go so as to realize their greatest mutual separation?
Answer:
There are several ways to interpret the problem. The most common solution involves putting the four brothers at the vertices of a regular tetrahedron inscribed in the sphere of the earth. This solution is mimicked in nature by the arrangement of four hydrogen atoms surrounding a carbon atom in a molecule of methane.
74. RIVER-HAT PROBLEM.
You are paddling your canoe upstream at a constant velocity. After paddling for six miles, the wind blows your hat into the stream and the hat begins flowing downstream. You continue to paddle upstream for two more hours before noticing that your hat is missing, at which time you turn around and paddle downstream at the same rate you had paddled upstream, overtaking your hat just as you return to your original starting point. What is the speed of the current?
Answer:
Let c be the speed of the current, b the speed of the boat (in stillwater). The time it took for the hat to float back to its startingpoint is 6/c. The distance the boat travelled (upstream) in the two hour period after losing the hat is 2(b - c) miles, so the total upstream distance travelled is 6 + 2(b - c). During the return trip the boat was moving at a rate of (b+c) so the time from when the hat was lost until the return of the boat to the starting point was [6 + 2(b - c)]/(b + c) + 2. Setting this quantity equal to 6/c and solving gives c = 1.5, independent of b.
Aliter: Relative to the water, the hat stays still. So, again relative to the water and hat, the rower moves just as fast upstream as downstream. After the hat dropped, the rower rowed for four hours and the hat moved six miles, so the current is flowing at a rate of 6/4 = 1.5 miles per hour.
75. INSUFFICIENT GLOVES.
Three surgeons and a clumsy cook go camping in the remote wilderness. The clumsy cook stumbles over the campfire as he is serving the surgeons, injuring himself and dumping hot stew on the hands of the surgeons. The cook's injuries need surgical treatment. The surgeons' injuries are minor but open. It turns out they brought the equipment necessary for the cook's surgery with them, and they can use the campfire to sterilize the tools. But there are only two rubber gloves. Because of the different surgeons' skills, all three of the surgeons are needed to operate on the cook, in sequence. How can this be done without any of them being exposed to the blood of any of the others?
Answer:
The first surgeon operates with the first glove (glove A) inside the second glove (glove B). The second surgeon operates using just glove B. The third surgeon operates using glove A, turned inside out, inside glove B.
76. 4 SWITCHES AND 4 BULBS.
Four switches that are downstairs control 4 bulbs that are upstairs in a room. You do not know which switch controls which bulb. You are presently at the downstairs. These four switches can be turned on or off. Once you do a combination of 'on and off', then you can go upstair and see the bulbs and should find it out which switch is for which bulb without coming back.
Answer:
Turn on switches 3 and 4 and wait fifteen minutes or so. Then turnswitch 3 off, turn switch 2 on, and enter the room. If the bulb is dark and cool, switch 1 controls it. If the bulb is bright and cool, switch 2 controls it. If the bulb is dark and warm, switch 3 controls it. If the bulb is bright and warm, switch 4 controls it.
77. CHECK THE IMPOSSIBILITY.
Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.
Answer:
50 factorial includes, as factors, 10, 20, 30, 40, and 50. Therefore, the value of 50 factorial must end in at least five zeroes. The number given only ends in three zeroes. The correct value of 50 factorial is close to this, however. It's equal to
30414093201713378043612608166064768844377641568960512000000000000.
78. SITTING FARTHEST.
The Antisocial Club meets every week at Jim's Bar. Since they are so antisocial, however, everyone always sits as far as possible from the other members, and no one ever sits right next to another member. Because of this, the 25-stool bar is almost always less than half full and unfortunately for Jim the members that don't sit at the bar don't order any drinks. Jim, however, is pretty smart and makes up a new rule: The first person to sit at the bar has to sit at one of two particular stools. If this happens, then the maximum number of members will sit at the bar. Which stools must be chosen? Assume the stools are numbered 1 to 25 and are arranged in a straight line.
Answer:
The first person must take either stool 9 or 17 (because of symmetry, it doesn't matter which). Assume they pick seat 9. The next person will pick seat 25, since it is the furthest from seat 9. The next two people will take Seats one and 17. The next three will occupy 5, 13, and 21. The next six will occupy 3, 7, 11, 15, 19, and 23. This seats the maximum of 13 people, and no one is sitting next to another person. If a seat other than 9 or 17 is chosen first, the total bar patrons will be less than 13.
79. BOY'S FEAST.
If a boy and a half can eat a hot chicken and a half in a minute and a half, how many hot chickens can six boys eat in six minutes?
Answer:
Let's break the question down into steps. We know that a boy and a half can eat a hot chicken and a half in a minute and a half. So how manyhot chickens could six boys eat in a minute and a half? We have the same amount of time, but four times as many boys, so the answer is four times as many hot chickens -- six, to be precise. But now let's consider what six boys could eat in six minutes. We now have four times as much time, so the answer is four times as many hot chickens -- specifically, 24.
80. IMPOSSIBLE COMBINATION.
At John's Bakery, you can order Milky breads in boxes of 6, 9, and 20. What is the largest number of breads that it is not possible to obtain by purchasing some combination of these boxes?
Answer:
You can buy any number of breads that is evenly divisible by three except for three just by using combinations of boxes of 6 and boxes of 9. (Use at most one box of 9, then multiples of boxes of 6.). If the number is not divisible by three, use a box of 20. If, after a box of 20 is purchased, the remaining number is divisible by three, you're all set. Otherwise, use a second box of 20. The remaining number will necessarily be divisible by 3, and you're all set. So the largest number that cannot be purchased would be one that requires two boxes of 20 before the remainder is reduced to a number divisible by three. Since three is the only number evenly divisible by three that cannot be purchased, the largest impossible number is 3+ 20 + 20 = 43.