puzzles

  1. how to measure 45 minutes using two identical wires?

    • light two ends of one wire and one end of another wire, 1st wire burns out after 30 min. Now second would take 30 min to complete. As soon as 1st wire burns out completely, light the 2nd from other side,, now it will take 15 min. So you got 45 min.

  2. find ages of daughters.

    • the product of their age is 72
    • the sum of their ages is equal to house number (goes out and look at the house number and still cann’t know)
    • the oldest of the girls strawbarry ice-cream
    • 1 1 72=72; 1 2 36 =72; 1 4 18 =72; 1 6 12 =72; 1 8 9 =72; 2 2 18 = 72; 2 3 12 =72; 2 4 9 = 72; 2 6 6 = 72; 3 3 8 =72; 3 3 8 = 72; 3 4 6 = 72;
    • 1+1+72 =74; 1+2+36 = 39; 1+3+24 =28; 1+4+18=23; 1+6+12=19; 1+8+9=18; 2+2+18=22; 2+3+12=17;2+4+9=15; 2+6+6 = 14;3+3+8=14;3+4+6=13;
    • All sum are unique 14, so the age sum must have been 14; otherwise he would guessed the ages from the number of houses,and the have only one oldest girl. So we can get 3,3,8;

  3. pay an employee using a 7 units gold rod?

    • an employee works for an employer for 7 days, the employer has a gold rod of 7 units, how does he pays to the employee so that the employee gets 1 unit at the end of everyday. The employer can make at most 2 cuts in rod
    • cut 2 times, he can get 1,2,4; first day give 1; second day, take one back and give two; third day, give 1; fourth day; take 1,2 back and give 4, and so on.

  4. find the poisoned wine

    • you have 240 barrles of wine, one of which has been poisoned, after drinking the poisoned wine, one dies within 24 hours, you have 5 slaves whom you are willing to sacrifice in order to determine which barrel contains the poisoned wine. How would you do that?
    • number the barrels with 5 digit numbers consisting of 0, 1,2. 3**5 = 243 is larger than 240. Number the slaves as 1, 10, 100, 1000, 10000. Number 0 on a barrel represents the wine in the barrel will not be taken by the slave. Number 1 on a barrel represents the wine in the barrel will taken by the slave on 1st day. Number 2 on a barrel represents the wine in the barrel will taken by the slave on 2nd day.
    • let us say the barrel is numbered 11201, the wine in this barrel is taken on the first day by the slave numbererd 10000, 1000 and 1, it is taken on the second day by slave numbered 100, And it is not taken by the slave numbered 10. If the slave numbered 10000, 1000 and 1 die within first 24 hours, slave numbered 100 dies in the next 24 hours and the slave numbered 10 does not die. Then the poisoned barrel has to be 11201.

  5. 3 bulbs and 3 switches

    • there is a room with a door and three light blubs. Outside the room there are three switches, connected to the blubs. You may manipulate the switches as you wish, but once you open the door you cann’t change them. Identify each switch with its bulb.
    • Trun on switch X for 5 to 10 minutes, turn it off and trun on switch Y, open the door and touch the light bulb.
    • if the light is on, it is y. if the light is off and hot, it is X. if the light is off and cold, it is z

  6. find the jar with contaminated pills

    • you have 5 jars of pills, each pill weights 10 grams,except for a contaminated pills contained in one jar, which each pull weights 9 grams. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?
    • take out 1 pill from jar 1, 2 pills from jar 2, 3 pills from jar 3, 4 pills from jar 4 and 5 pills from jar 5. Put all these 15 pills on scale. If the weight is 149 then jar 1 is targeted, 148 then jar 2 is targeted, 147 then jar 3 is targeted, 146 then jar 4 is targeted, 145 then jar 5 is targeted.

  7. Monty hall problem.

    • Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
    • always swaping, if you donn’t swap, you have 1/3 to get the car, if you swap the choice, you cannot get the car only if you first pick is car(1/3), so you can get the car after swapping with a probabllity of 2/3

  8. Find the fastest 3 horses

    • There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out how many races are required to get the top 3 horses.
    • 共七次，先分成五队，找出最大的，每一组最后两名删掉（-10），5组最快的再赛一次，后两名所在的组删掉（-6），这样我们就得到了第一快的马，假设A组，A1,A2,A3, B组: B1,B2,B3, C组：C1,C2,C3.第一名A1，挑出来了， 从剩下的8匹再挑俩，c2,c3可以删了，b3，可以删了，这样A2, A3, B1, B2, C1 再赛一场，然后找前俩名就好了

  9. A Man with Medical Condition and 2 Pills

    • A man has a medical condition that requires him to take two kinds of pills, call them A and B. The man must take exactly one A pill and exactly one B pill each day, or he will die. The pills are taken by first dissolving them in water.The man has a jar of A pills and a jar of B pills. One day, as he is about to take his pills, he takes out one A pill from the A jar and puts it in a glass of water. Then he accidentally takes out two B pills from the B jar and puts them in the water. Now, he is in the situation of having a glass of water with three dissolved pills, one A pill and two B pills. Unfortunately, the pills are very expensive, so the thought of throwing out the water with the 3 pills and starting over is out of the question. How should the man proceed in order to get the right quantity of A and B while not wasting any pills?

    • add one more A pill into the glass and take half today and take half tomorrow. It works under the following assumptions: the dissolved Pills can be used next day; The man has to take pills at least for one more day.

  10. You are blindfolded and 10 coins are place in front of you on table. You are allowed to touch the coins, but can’t tell which way up they are by feel. You are told that there are 5 coins head up, and 5 coins tails up but not which ones are which.

    • Can you make two piles of coins each with the same number of heads up? You can flip the coins any number of times.
    • Make 2 piles with equal number of coins. Now, flip all the coins in one of the pile. If there is x head, 5-x tail in one pile, 5-x head, x tail in another pile, flip first pile, we get x tail, 5-x head, the same as second pile.

  11. There are 4 persons (A, B, C and D) who want to cross a bridge in night.

    • A takes 1 minute to cross the bridge.
    • B takes 2 minutes to cross the bridge.
    • C takes 5 minutes to cross the bridge.
    • D takes 8 minutes to cross the bridge.
    • There is only one torch with them and the bridge cannot be crossed without the torch. There cannot be more than two persons on the bridge at any time, and when two people cross the bridge together, they must move at the slower person’s pace,Can they all cross the bridge in 15 minutes?
    • A and B cross the bridge. A comes back. Time taken 3 minutes. Now B is on the other side.
      C and D cross the bridge. B comes back. Time taken 8 + 2 minutes. Now C and D are on the other side.
      A and B cross the bridge. Time taken is 2 minutes. All are on the other side.Total time spent is 3 + 10 + 2 = 15 minutes.

  12. There are 1000 wine bottles. One of the bottles contains poisoned wine. A rat dies after one hour of drinking the poisoned wine. How many minimum rats are needed to figure out which bottle contains poison in hour.

    • 10 rats, We need to figure out in hour. We need 10 rats to figure out the poisoned bottle. The result is based on binary number system. We get 10 using ⌈ Log21000 ⌉.