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Posts posted by bonanova

  1. At lunch yesterday four students, Al, Bill, Jack and Tom (last names Conner, Morgan, Smith and Wells, in some order) amused themselves by dealing poker hands to all, with the winner being the holder of the best hand. The winner of the first hand was to collect 10 cents from the other three; the second-game winner would collect 20 cents each; the third winner get 30 cents each; and so on. When the bell rang for afternoon classes to begin, four hands had been dealt, with each student winning once, in this order: Jack, Morgan, Bill and Smith. At the outset Tom had the most money, but at the end Wells had the most.

    What are the students' full names?


  2. OK these subtractions do not work using letters.
    But make a number substitution, the same for both,
    and everything's fine.

    N I N E             N I N E
    - T E N             - O N E
    =======             =======
      T W O               A L L

  3. The local Literary Society had just enough members to field two teams, and so they decided one Saturday in June to play a baseball game down at the park. After members were assigned to teams, aptly named the Prose and the Cons, they purposed to determine which team would be the home team in a sort-of literary manner. The 18 players formed a circle and began counting, clockwise, using the letters of the alphabet rather than numbers. It was decided that if the "count" ever got to "Z" the next player would continue by calling out "A" and so on. The process would continue until a player named the letter that was also his initial. That player would then gain the honor of having his team bat last. The captain of the Cons went first, calling out "A", the next player called "B", and so it went.

    Surprisingly, after 360 letters were called no player had called his initial. Well, said one, it was a nice thought, but hey let's just flip a coin, already. And thus the Prose were named home team. But by then it was dark, and the game was accordingly postponed until the following weekend.

    But when they gathered next to play, there was a disagreement about who was on which team, owing to the fact that no one had bothered to write the rosters down.

    No problem, though. All 18 members of the Lit Soc, Taylor, Brown, Jenkins, Miller, Gerson, Babcock, Adams, Randolph, Carver, Smith, Flynn, Sawyer, Timmons, Myers, Lucas, Morton, Young and Peters, were also long time members of BrainDen and thus had no difficulty at all in reconstructing the team rosters.

    And neither should you. Who played for each team?

  4. Four men, Brown, Harris, Jones and Smith, were talking one day over drinks about their sons. Among the statements they made, some were true and others were false, owing to the fact the they didn't know their friends' sons all that well. The only thing we know for sure is that each statement in which the speaker mentions the name of his own son is reliably true.

    1. Brown:
      Al graduates from High School next month.
      Carl hasn't had a vacation since he started working two years ago.
      Bill's wife can't get him to take any kind of exercise.

    2. Harris:
      Bill is going to be married next spring.
      Dick has been dating my daughter.
      Al and Carl played on the freshman football team at college this year.

    3. Jones:
      Al will be nine tomorrow.
      Bill is younger than Al.
      Carl and Dick are returning from a hunting trip today.

    4. Smith:
      Bill and Jones won the Father and Son Handball Tournament.
      Dick told me yesterday that he hasn't seen Carl for a long time.
      Al and Carl were roommates at college last year.

    What is the full name of each boy?

  5. You know the drill. Generally they tell the truth, but sometimes they lie. For Bill the lying days are Monday, Tuesday and Wednesday. For his brother John, the lies are told on Tuesday, Thursday and Saturday. 

    Recently the three of us had a chat:

    Me: Hi, what’s your name?

    Older brother: I’m Bill. 

    Me: What day is it?

    Older brother: Yesterday was Sunday. 

    Younger brother: And tomorrow is Friday. 

    Me: Wait. That doesn’t add up. Are you sure you’re telling me the truth?

    Younger brother: I always tell the truth on Wednesdays  

    What day was it, and what is the name of each boy?


  6. Spoiler

    I miscalculated a combination and transposed a 9 and 7.
    fixed the combination and trustingly? kept my transposition.

    One more try ...


    The Selection pool comprises 20 players: { SS III FFFF BBBBB GGGGGG }
    Removing the captain and goalkeeper the pool shrinks to 18:
    Without the three-German restriction, we have 18 choose 9 =
    48620 different teams.

    We must include {3 4 5 6} Germans, then choose {6 5 4 3} from the 12 non-Germans.

    (6 choose 3 = 20) x (12 choose 6 = 924) = 18480
    (6 choose 4 = 15) x (12 choose 5 = 792) = 11880
    (6 choose 5 =  6) x (12 choose 4 = 495) =  2970
    (6 choose 6 =  1) x (12 choose 3 = 220) =    220
    TOTAL                                  33550 different teams


  7. Spoiler

    The Selection pool comprises 20 players: { SS III FFFF BBBBB GGGGGG }
    Removing the captain and goalkeeper the pool shrinks to 18:
    Without the three-German restriction, we have 18 choose 9 =
    48620 different teams.

    We must include {3 4 5 6} Germans, then choose {6 5 4 3} from the 12 non-Germans.

    (6 choose 3 = 20) x (12 choose 6 = 924) = 18380
    (6 choose 4 = 12) x (12 choose 5 = 792) =  9504
    (6 choose 5 =  6) x (12 choose 4 = 495) =  2790
    (6 choose 6 =  1) x (12 choose 3 = 220) =    220
    TOTAL                                  30994 different teams


  8. With a tip of the hat to @BMAD  for his interesting puzzle.

    For your amusement, here's an interesting spin on this genre:

    One night you encounter a two-hour traffic delay due to an accident (the tow truck had difficulty clearing the road.) So, for a time interval 13 of two hours you were constrained to travel at 0 mph. You called home and said, sorry dear, but I'll be two hours late getting home. 

    The next night, for some unimaginable reason, you were also constrained to travel part of the way at 0 mph, this time for a distance of one inch. What do you say now when you call home?

    • Like 1

  9. On 4/2/2019 at 12:50 AM, Thalia said:


      Hide contents

    Does the 2nd word have to be the plural of the 1st word or can it be a different word?

    "Becomes plural by removing it." Could that mean removing the letters "i-t"?



    I'll answer both in the clear.

    No. (although the words I have in mind, one plural, one singular, are closely related)

    No. It's the literal removal of an "s".


    On 4/2/2019 at 7:02 AM, rocdocmac said:
      Hide contents

    brass - s = bras


    Playing with singulars and plurals I arrived at these facts ,,,

    If the plural of mouse is mice and that of louse is lice,  then the plural of house must be hice and the singular of rice must be rouse.

    Kudos. But not the words I had in mind. They are common words, and they are closely related.

  10. Appears to be ...


    Simplify to dividing 5 sausages for 3 people

    Denote a third of a sausage (whether cut or uncut) by [3].
    Denote an uncut sausage by [3][3][3] and an intact 2/3 of a sausage by [3][3].

    Three persons would be optimally served as follows:

    1. [3][3][3]  [3][3]
    2. [3][3][3]  [3]  [3]
    3. [3][3][3]  [3][3]

    The black sausages were not cut.
    Two sausages, the red one and the green one, were each cut once, creating four pieces.

    Do this 6 times.

    12 cuts will have created 24 pieces.


  11. The solutions are


    1 and 2.




    x 1/x = (x2)1/x^2 = x 2/x^2

    By inspection 1 and 2 are solutions, and a plot of the difference of x 1/x and x 2/x^x shows sign changes (only) at 1 and 2.

    Also, for any value of x not equal to 0 (illegal division) or 1 (all powers of 1 are equal) dividing by x yields simply

    1/x = 2/x2 or more simply 

    x2 = 2x.


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