2 Points for Each Puzzle

Two trains start at the same time, one from London to Liverpool, the other from Liverpool to London. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

A gentleman who recently died left the sum of $8,000 to be divided among his widow, five sons, and four daughters. He directed that every son should receive three times as much as a daughter, and that every daughter should have twice as much as their mother. What was the widow’s share?

A certain Sultan wished to send into battle an army that could be formed into two perfect squares in twelve different ways. What is the smallest number of men of which that army could be composed? To make it clear to the novice, I will explain that if there were 130 men, they could be formed into two squares in only two different ways—81 and 49, or 121 and 9. Of course, all the men must be used on every occasion.

“All cannon-balls are to be piled in square pyramids,” was the order issued to the regiment. This was done. Then came the further order, “All pyramids are to contain a square number of balls.” Whereupon the trouble arose. “It can’t be done,” said the major. “Look at this pyramid, for example; there are sixteen balls at the base, then nine, then four, then one at the top, making thirty balls in all. But there must be six more balls, or five fewer, to make a square number.” “It must be done,” insisted the general. “All you have to do is to put the right number of balls in your pyramids.” “I’ve got it!” said a lieutenant, the mathematical genius of the regiment. “Lay the balls out singly.” “Bosh!” exclaimed the general. “You can’t pile one ball into a pyramid!” Is it really possible to obey both orders?

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~ by wcuk on August 22, 2008.

8 Responses to “2 Points for Each Puzzle”

  1. 4. The soldiers must only use 4900 cannonballs. 1+2^2+3^2+4^2+5^2+6^2+7^2…+24^2=4900. Do they have that many cannonballs, or a ladder high enough to stack them 70 high? Who knows?

  2. I figured out the answer to all of this… Will is trying to beat us all to graduation by distracting us as we return from lunch. How devious!!!

  3. Real World Solutions:

    1. The London train never leaves the station after someone mistakes an iPod charger for an I.E.D.
    2. After several paternity challenges and lawyers fees the widow owes $10,223
    3. When a certain Sultan realizes he is late for honey-wrestling night in his harem he declares that any shape army will do.
    4. When one soldier jokes, “Look at you lads playing with yer balls!” the order is changed to arrange them in unassuming straight lines.

  4. The fools on the Liverpool-bound train were all Chelsea Blues fans. They realized that it was a home match for them that weekend and had to catch a London-bound train immediately after getting to Liverpool. This was a fortunate turn of events because Liverpool delivered a sound thrashing to Chelsea at a half-empty Stamford Bridge — so bad was the defeat that had any Chelsea supporters been there to witness it, there would have been suicide and mass rioting to follow. Thank the Lord for the stupidity of Chelsea fans.

  5. Train 1 is running twice as fast as train 2.

  6. The widow gets ~205 clams. Assumes that the widow was the mother of all 9 children.

  7. 160225 soldiers:
    225, 160000
    1024, 159201
    5776, 154449
    6561, 153664
    12769, 147456
    19600, 140625
    30625, 129600
    33489, 126736
    46656, 113569
    51984, 108241
    63504, 96721
    70225, 90000

  8. 1. 2 points for Mr. Mistoffelees

    2. 2 points for Mr. Mistoffelees (And a stern warning for omitting decimal places)

    3. 2 points for theJenksster

    4. 2 points for Charlie

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