Richard's Stumpers

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Set #5

  1. In a collection of sheep and turkeys, there are a total of 43 heads and 120 feet. How many of each animal (sheep and turkey) are there in the lot?

  2. A certain number leaves a remainder of one when it is divided by 2, 3, 4, 5, or 6, but leaves no remainder when it is divided by 7. What is the smallest number that solves this problem?

  3. It is said that Diophantus passed 1/12 of his life in infancy and 1/6 more in youth. Then he married and spent 1/7 of his life and 5 more years. Then he had a son whom he survived by 4 years. The son reached only half the father's age. How old was Diophantus when he died?

  4. A man had two clocks. One clock did not run at all and the other lost four minutes every day. Which clock is more often correct? Explain your answer!!

  5. At a fork in the highway, one road leads to the town of Truth where the inhabitants tell only the truth. The other road leads to the town of Lies where the inhabitants tell nothing but lies. A traveler doesn’t know which road leads to which town and there is only an old man at the fork whom he can ask. The traveler is in a hurry to reach the town of Truth and only has time for one question. Not knowing whether the old man is from Truth or Lies, what should the traveler ask him in order to find his way?

  6. In an ancient kingdom lived a princess as beautiful as her father was cruel. Lovers came from far and wide to seek her hand in marriage. To each the King offered the following test: The King will place two slips of paper in a hat. On one slip he will have written the word LADY and on the other he will have written TIGER. In a public arena the lover will draw one slip from the hat. If the slip reads LADY he may marry the princess. If it reads TIGER, he is tossed into the royal menagerie at mealtime.

    Many admirers accepted the test. They all ended as tiger food, for the King simply wrote TIGER on both slips.

    Eventually the princess fell in love with one of her lovers and told him why he could not possibly win the test. Inspired by true love, the young man accepted the test and managed to win without exposing the King’s trickery. How did he do it?

  7. In the following addition problem each of the x’s represents a different digit. One of the x’s has already been replaced by ‘3’. Complete the problem finding which digit goes with which x. 

         3xx  +  xxx  =  xxxx.

  8. An object is in motion through a stationary medium. If the surrounding medium were absent, the object would continue moving indefinitely at the same speed. However, because of the energy lost as friction with the medium, the object speeds up. Explain what could be actually happening for this to occur?

    Answers are available with Stumper Set #6.

Answers to Stumper Set #4

  1. Smith is the navigator.

  2. 15 apples

  3. 7 people

  4. It doesn’t make any difference.

  5. 16 lbs.

  6. ‘indivisibility’

  7. 1728 cubes

  8. 927 x 63 = 58401

  9. 1, -1, 2, -2, 3

  10. 13