Brainteasers

By the way, I am a great fan of non-trivial mathematical puzzles, try some of the listed ones below.

1. Fruit for Africa produces two gift packages of fruit.
   • Pack A contains 20 peaches, 15 apples and 10 pears.
   • Pack B contains 10 peaches, 30 apples and 12 pears.
   • The company has 40000 peaches, 60000 apples, 27000 pears.
   • The profit on pack A is $2.00 and on B it is $2.50.
   Assuming that all fruit packaged is sold (no theft or goes bad), what number of packages of A and B should be prepared to maximise the profit? What will the profit be? How much fruit and of which types will be left over?
   
   

   Answer:Warm up with this one.

2. A man walking his dog along a straight country road spots a friend in the distance. The dog sprints ahead to greet her. As soon as it arrives, the dog turns and runs straight back, then turns and runs back to the girl who is nearer by now. The dog continues running this way until the two meet. Given that initially they were a kilometre apart, and each walks at a steady pace of three kilometres an hour, and the dog runs at nine kilometres an hour, how many trips did the dog make, and what total distance did he cover?
   
   

   Answer: If the dog keeps turning and running he can theoretically make an infinite number of trips. He halves his trip distance at each turn. He will however be running at a costantly reducing distance and will be limited by the time taken to turn around. No matter what, he only covers a finite distance of 1.5 km because of his velocity of 9km/h and the fact that they take 10 minutes to meet each other. In practice he would make no more than about 10 trips. His 11th trip is only .7 of a meter which is the length of the dog. Maybe 12 trips if it is a small dog and no more than 13 if it is a Sandton mini-rat Chihuahua!

   
   
3. One day Kerry celebrated her birthday. Two days later her older twin brother, Terry, celebrated his birthday. Why?
   

   Answer: At the time she went into labour, the mother of the twins was travelling by boat. The older twin, Terry, was born first early on March 1st. The boat then crossed a time zone and Kerry, the younger twin, was born on February the 28th. Therefore, the younger twin celebrates her birthday two days before her older brother.

   
   
4. A father and his son marries a mother and her daughter. The father marries the daughter, whilst the son marries the mother. What relationship is the son of himself?
   

   Answer: His own grandfather. Because he married the mother, he is the (step)father of the daughter, and therefore the (step)father-in-law of her husband, which is his father. Well, the father-in-law of your father is your grandfather.

   
   
5. A tramp, unable to afford cigarettes, collects butt-ends and shreds them until he has sufficient tobacco to make a real cigarette. He need seven butts to make one whole cigarette. One day he finds four butts in the gutter, and an additional eight in the trash bin, three in a waste basket and five in a restaurant ash tray. He has enough money for a drink and manages to collect 15 more butts in the bar. He discovers four more in the unemployment office, six more on the way home, and four in the pocket of an old coat. How many whole cigarettes was he able to smoke that day?
   

   Answer: answer is eight, where does the last one come from? Well after smoking the 7 cigarets he made, he has 7 more butts to make one more, i.e. a total of 8 cigarettes.

   
   
6. A prison warden had the following security principles:
   • There must be twice as many prisoners on the top floor than on the bottom,
   • no cell could be unoccupied,
   • there must always be 11 prisoners in the six cells on each of the four sides.

   One night 9 prisoners escaped. Yet, the next morning when the warden made his rounds, nothing seemed amiss. How many prisoners were there to begin with? How did the remaining prisoners rearrange themselves to conceal the escape? There are two floors and the building is square. There are three cells per floor on every side (24 cells in total).

   Answer: Send me US$100.00 for this one!

7. There is a guy who lives in his house by himself. He rarely leaves his house. After two weeks, he runs out of food so goes to the store to get more. Upon leaving, he turns off the TV & lights. He returned the next morning. However, that night 100 people died because of him, how could this be so?
   

   Answer: He lives in a lighthouse

8. You fall into a pit nine metres deep. Every day you climb three metres and in the evening while you sleep you fall two metres back again. On which day do you reach the top?
   

   This is easy, work it out.
   If you enjoyed them please send me few lines

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