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Math Support at the Academic Success Center

Richard's Stumpers

Set #2

  1. "I seem to have overdrawn my account." said Mr. Green to the bank president, "though for the life of me I can’t understand how this happened. You see, I originally had $100 in the bank, then I made six withdrawals. These withdrawals add up to $100, but according to my records there was only $99 in the bank to draw from. Let me show you the figures." Mr. Green handed the bank president a sheet of paper on which he had written the following:

    Withdrawals         Amount left in the bank

    $50                                $50

    $25                                $25

    $10                                $15

    $ 8                                 $ 7

    $ 5                                 $ 2

    $ 2                                 $ 0


    $100                             $ 99

    "As you can see," said Mr. Green, "I seem to owe the bank a dollar." The bank president looked over the figures and smiled, "I appreciate your honesty, Mr. Green, but you own us nothing." "Then there’s a mistake in the figures?" asked Mr. Green. "No, your figures are correct," said the president.

    Can you explain where the error lies?

  2. A man observing a portrait says, "Brothers and sisters have I none, but that man’s father is my father’s son." How is this possible?

  3. Find a number of two digits that is equal to twice the sum of its digits?

  4. During Christmas vacation a boy went to the movies. At the box office he asked if he was young enough to be admitted for half price.

    "How old are you?" the cashier asked.

    Being an honest young man, he replied, "The day before yesterday I was 11, and next year I will be 14."

    If tickets were half price for anyone 12 or under, did he get in for half price? Also, on what day of the year did he go to the movies?

  5. A rubber ball is known to rebound half the height that it drops. If a ball is dropped from a height of 50 feet, how far will it have traveled by the time it hits the ground the fourth time?

  6. There are two telephone poles, each 100 feet tall above level ground. A 100 foot long cable is strung between the poles with each cable end fastened at the top of each pole. Between the poles, the cable sags to 50 feet from the ground. How far apart are the poles?

  7. I woke up one night and heard my clock strike ‘one’. I was too lazy to turn on the light to see what time it was. As I lay there pondering, it occurred to me to speculate how long I would have to lie awake in order to be sure what the exact time was. My clock strikes the hours and strikes ‘one’ each half hour. I fell asleep before I solved the problem, but can you work out what is the longest time I would have to lie awake after hearing the strike ‘one’ to be sure of the time?

    Answers are available with Stumper Set #3.

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Answers to Stumper Set #1

  1. A box bounced out, tumbled end over end to the torrent below and came swirling back past the police car.   This is not possible because they were going downhill which means that the box should have gone down the hill, not up past the police car.

  2. Father is 40 years old and the son was 8 years old.

  3. He bought 1 cow, 9 hogs, and 90 sheep.

  4. There are 3 different possibilities: 2 in 16 and 4 in 17  or  2 in 16 and 2 in 9 and 1 in 21 and 1 in 29 or 2 in 16 and 2 in 21 and 1 in 9 and 1 in 17.

  5. Strengths

  6. Tilt the barrel over until the water is at the edge where it spills out and is just touching the bottom corner of the barrel.

  7. The number of cars that passed was 23.

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Set #1    Set #2    Set #3    Set #4    Set #5    Set #6    Set #7    Set #8    Set #9    Set #10    Set #11    Set #12    Set #13    Set #14    Set #15    Set #16    Set #17    Set #18    Set #19    Set #20    Set #21    Set #22    Set #23    Set #24

 

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