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Posts posted by bonanova

  1. You want to send a valuable object to a friend.

    You have a box to contain the object.

    The box has a locking ring which is more than large enough to have a lock attached.

    You and your friend have several locks with keys.

    But your friend does not have the key to any lock that you have, and vice versa.

    How do you do it?

    Note that you cannot send a key in an unlocked box, since it might be copied.

  2. You live in Killville - a town populated by 10 killers and 10 pacifists.

    When a pacifist meets a pacifist, nothing happens.

    When a pacifist meets a killer, the pacifist is killed.

    When two killers meet, both die.

    Assume meetings always occur between exactly two persons

    and the pairs involved are completely random.

    Are your odds of survival better if you are a killer? or a pacifist?

    Or does it matter?

    Regardless of whether you are a pacifist or a killer,

    you may disregard all events in which a pacifist other than yourself is involved

    and consider only events in which you are killed

    or a pair of killers other than yourself is killed.

  3. Sorry in advance if these are posted on here already. I took a quick look and didn't see any of them so here goes...

    1) A woman gave birth to two girls an hour apart on the same day of the same month of the same year, but the boys [sic] were not twins. How can this be?


    2) There are 5 paths through the woods. You can walk 100 feet down path 1, Path 2 and 3 are equal, Path 4 you can walk 200 feet down, and path 5 is 1/2 the size of path 1.

    The shortest path is 50 feet. How many paths can you walk down 50 feet?

    all 5

    3) The city of Dorkus passed an ordinance that nobody living within the city limits can be buried in the local cemetary.

    It costs thousands of dollars more to be buried in the next closest cemetery, but nobody complained about the ordinace.


    most living people don't want to be buried, and most dead people don't complain

  4. Question -- are you allowed to look at the table, and use row/col sorts to make the table sorted???

    If so, you can use sort_up and sort_down to manipulate numbers to their correct positions, much like solving the "15" puzzle.

    I'm assuming you're asking for a procedure to sort tables that could be programmed to sort any and all tables without human "guidance".

  5. Many impossible combinations can be eliminated from the given conditions:

    Since the digit 0 is not present, the 5th digit must be 5.

    The odd digit places then are 1 3 7 9 in some order because

    the even digit places must be even - 2 4 6 8 in some order.

    Each group of 3 digits must be a multiple of 3, meaning their digits sum to 3, 6, or 9.

    All combinations of digits 1-9 are divisible by 9.

    That takes care of dividing by 9, 5, 3, 2, and 1.

    The only divisors that must be checked are 8, 7, 6 and 4.

    For the middle three digits to sum to a multiple of 3 they

    must be [258] or [456] - where [abc] stands for either abc or cba.

    So the possibilities to check are

    [147] [258] [369]

    [369] [258] [147]

    [129] [456] [387]

    [387] [456] [129]

    [183] [456] [729]

    [729] [456] [183]

    Dividing the first seven digits by 7 eliminates almost all of these,

    and dividing the first 6 digits by 6 brings it down to only one,

    which also turns out to satisfy 8 and 4.

    381 654 729

  6. I heard this one a long time ago. :mellow:

    A man aproaches you in a dark alley. He says,

    "If you tell a lie, I will kill you with a knife. If you tell the truth, I will kill you with a gun."

    What do you say to stay alive?

    This has been posted in a slightly different form elsewhere in this forum.

    The usual answer is

    make a statement that is true if he uses a knife and false if he uses a gun.

    Several ways to construct such a statement. e.g. You will kill me with a knife, but you won't kill me with a gun.

    A much easier solution is

    Recognize that only declarative statements have a truth value.

    Don't make a declarative statement; that way it won't be the truth or a lie.

    Here are three possibilities:

    [1] Remain silent. - or if you must say something, ask a question

    [2] Why do you want to kill me? - or exclaim something:

    [3] No! Please do not kill me!

  7. Anyone find a lower one that divides into whole apples?
    No. Your answer is the right one.

    After a little math, you can show that the final share has to be 1 less than a power of 2.

    A simple program to calculate the other shares does not give integral values for 15, 31, 63 or 127,

    but does for 255: -> 255 319 399 499 624 ---> 3121.

  8. There's no "ravel" or "shape" operator in this puzzle. It only has "sort" operator to sort a column or a row.
    By sorting rows then columns [or v.v.] you get the smallest number to the upper left and the largest number to the bottom right, and all rows and columns sorted. Repeated sorts of rows and columns have no effect. Elements of the array are not sorted except within a row or a column.

    e.g. sort rows: then sort cols:

    6 9 4 3 ....... 3 4 6 9 ....... 1 2 4 7

    8 2 1 5 ....... 1 2 5 8 ....... 1 3 5 8

    7 6 5 4 ....... 4 5 6 7 ....... 3 4 6 8

    8 1 4 3 ....... 1 3 4 8 ....... 4 5 6 9

    Sorting row1, col1, row2, ... col4, the result is sorted rows and cols, but not sorted table:

    1 1 4 7

    2 3 5 8

    3 4 5 8

    4 6 6 9

    Once you reach a configuration where rows and cols are sorted, repeated sorting makes no change to the table.

    If that's all you can do, you're left with an unsorted table.

    To sort the table, you have to do something more than / different from sorting rows or cols.

    [a] sort diagonals or mess with its shape somehow.

  9. Ah, I think I get it now. The fallicy is juxtaposing the well ordered principal and the concept of "the smallest

    number not specifiable using fewer than 23 syllables" to define an empty set. Sorry I was so slow on that one.

    Not at all.

    Re-reading my post, I don't think I made the connection clear; tossed it in as a teaser, kind of ...

  10. Since Berry's Paradox leads the conclusion that there are only a finite number of integers, we must then conclude that

    d) there will be a final episode of General Hospital.

    However, since we know that d is impossible, we enter an entirely new kind of paradox.

    I read your post way too fast, and missed [d].


    Now, who's gonna tell the producers?

  11. I think I am somehow missing something, and have an observation.

    First, I get the paradox part, and did from the beginning, but I've never seen how

    Thus the set of all numbers is finite.

    Really, we are trying to define ALL numbers thus:

    [1] the set of all numbers that can be described using fewer than 23 syllables - a finite set [since 23 is finite.]

    [2] the set of all numbers that cannot be described using fewer than 23 syllables - by WOP, the empty set

    Now we only found the SMALLEST of the numbers defined by #2,

    but there are an infinite amount that go above that number,

    many of which I am sure cannot be described using fewer

    than 23 syllables when written out in any way.

    You say that you saw the paradox, but you say we did find the smallest number .... etc.

    The paradox says that we did not find ... [nor can anyone find - nor is there]

    the smallest number not describable using fewer than twenty-three syllables.

    Since that set lacks a smallest member it is the empty set.

  12. I claim it's how we describe categories of things.

    No math needed...

    If you choose 4, you can ignore that as well.

    ALL of the customers love the food. Because you can't find ONE that doesn't. and ...

    NONE of the customers love the food. Because you can't find ONE that does.

    It's logically ok to use universal quantifiers [all, no, none] with empty sets.

    But you can't use particular quantifiers [one, some] with empty sets.

    How about "Some of the customers love the food, because you can neither find a specific one that does, nor doesn't."

    "Some" means "at least one."

    And there isn't one.

    Read existential import.

    You can talk about all of nothing and about none of nothing.

    But you can't talk about some of nothing.

  13. OP states .... Furthermore, the father's age is a multiple of the son's age.

    If multiple does not mean integral multiple, the statement gives no information.

    Every pair of ages, otherwise, could be described as multiples.

    So if you reject that as precise, let's affirm it for all practical purposes. :D

    1. You cannot ask a "puzzle question" to be "precised".

    2. Furthermore, if father's age is 46 years old and son's age is 20 years old, the father's age is a multiple of the son's age when we "precisely" count the age into minutes or seconds. Therefore, besides the father is older enough to give a birth, the son could be 10, 12, 16, 20 or other normal ages. :)

    Nope, nope, and ... nope.

    Not unless you assume the question asks the ages in those units for which the multiples are integral -- minutes, seconds.

    You obviously did not assume that -- years are the only units mentioned in your answer.

    You're dancing around the issue pretty well, but you're running out of places to hide. :D

    Precision or looseness aside, it's nice to be consistent. B))

  14. For the cut-pieces of a rectangle to form triangles, the cuts must pass thru corners [not sides].

    Only two such cuts exist - along the two diagonals.

    That gives you 4 triangles, not 5.

    The only other way to cut a rectangle is to cut it after it has been folded.

    All my tries at this so far have led to an even number of triangles.

    I'll keep trying.

  15. OP states .... Furthermore, the father's age is a multiple of the son's age.

    If multiple does not mean integral multiple, the statement gives no information.

    Every pair of ages, otherwise, could be described as multiples.

    So if you reject that as precise, let's affirm it for all practical purposes. :D

  16. There are 4 balls marked as "A", "B", "C" and "D" in the order. So, randomly draw one out and then put it back to the

    next draw position. For example,

    ABCD -> 3 ©

    CABD -> 3 (B)

    BACD -> 4 (D)

    DACB -> 2 (A)

    So, the question is, how to calculate the final stage with a given draw sequence with minimum draw simulation?

    OK. It looks like what you do is

    [1] remove a ball at random

    [2] re-arrange the other balls into their original order [e.g. ACD in line 3] but ... not ACB in the last line. I don't get that part.

    [3] replace the removed ball at the beginning [left end] of the line.

    OK now what are you asking? Can you rephrase it or give an example? Thanks.

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