1. Subscribervenda
    Dave
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    04 Dec '21 10:11
    In a poll of mindset solvers,exactly two - sevenths said they liked question 1 best:an exact number of fifths(more than none)said they liked question 2 best;700 said they liked question 3 best.How many were polled
  2. SubscriberBigDogg
    Father Mocker
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    04 Dec '21 18:16
    @venda

    2p/7 + xp/5 + 700 = p

    x and p are integers

    solve for p:
      10p + 7xp + 24500 = 35p
      7xp + 24500 = 25p
      25p - 7xp = 24500
      (25 - 7x)p = 24500
      p = 24500 / (25 - 7x)

    prime factors of 24500:
      2*2*5*5*5*7*7 = 24500

    if x = 1, the denominator is 18; 18 is not a factor of 24500
    if x = 2, the denominator is 11; also not a factor
    if x = 3, the denominator is 4; this IS a factor
    if x >= 4, the denominator is negative, leading to negative people polled

    x = 3, p = 6125
  3. Subscribervenda
    Dave
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    04 Dec '21 19:49
    @bigdogg said
    @venda

    2p/7 + xp/5 + 700 = p

    x and p are integers

    solve for p:
      10p + 7xp + 24500 = 35p
      7xp + 24500 = 25p
      25p - 7xp = 24500
      (25 - 7x)p = 24500
      p = 24500 / (25 - 7x)

    prime factors of 24500:
      2*2*5*5*5*7*7 = 24500

    if x = 1, the denominator is 18; 18 is not a factor of 24500
    if x = 2, the denominator is 11; also not a factor
    if x = 3, the denomin ...[text shortened]... factor
    if x >= 4, the denominator is negative, leading to negative people polled

    x = 3, p = 6125
    Excellent big dogg.
    Correct
  4. Subscribervenda
    Dave
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    19 Dec '21 10:29
    Must be a first!
    No mention of 700 in this weeks puzzle:-
    The three kings bought gifts of gold frankincense and myrrh, but forgot to agree who would bring what.Caspar and Melchior both bought one at random.Balthazar bought 2(hoping to re-gift the other)What are the chances that each king was able to present a different gift
  5. SubscriberPonderable
    chemist
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    19 Dec '21 15:14
    @venda

    It's that season 😉

    So the probability that Caspar and Melchior get the same is one in three.
    The probabiliyt that Beltsazar is getting the same pair as Capsar and melchior is also one in three, so we have a combined chance of 4 in 9 that they have the correct set to present.
  6. Subscribervenda
    Dave
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    19 Dec '21 19:24
    Well done Pondy
  7. Subscribervenda
    Dave
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    07 Feb '22 09:25
    I don't even understand the question this week but I'm sure some of you will.We're back to the 700 thing again! :-
    A legion of soldiers consists of several cohorts? of 700 soldiers.
    A legion could form a wedge with one soldier on the first rank,two on the second and so forth.
    What is the smallest size that a legion could be ?
  8. SubscriberPonderable
    chemist
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    07 Feb '22 11:061 edit
    @venda


    If I understand correct, then row three would be three soldiers.
    So the question is when is the sum off all integers starting from one divisible by seven.
    Reveal Hidden Content
    After 175 rows we have have 15400 soldiers. They are organized in 22 Cohorts.


    in fact I wrote a little formula into Excel to find the numbers.
  9. Subscribervenda
    Dave
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    07 Feb '22 12:39

    Removed by poster

  10. Subscribervenda
    Dave
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    07 Feb '22 12:41
    Correct my friend.
    I removed the previous post 'cos it showed the hidden content!
  11. Subscribervenda
    Dave
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    27 Feb '22 09:54
    A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
    What is the smallest number of stripes that it could have
    I suspect it's a bit like the map problem where each adjacent country had to be a different colour
  12. SubscriberBigDogg
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    28 Feb '22 04:241 edit
    @venda said
    A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
    What is the smallest number of stripes that it could have
    I suspect it's a bit like the map problem where each adjacent country had to be a different colour
    I'm not quite understanding the stipulation. I envision a bunch of horizontal color bars stacked up, but then not every color is adjacent to every other color.
  13. Subscribervenda
    Dave
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    28 Feb '22 09:23
    @bigdogg said
    I'm not quite understanding the stipulation. I envision a bunch of horizontal color bars stacked up, but then not every color is adjacent to every other color.
    No. I didn't understand it either.I think the wording is a bit ambiguous.
    I'll post the given answer and explanation hidden
    Reveal Hidden Content
    11. On an n stripe flag there are n-1 places where two stripes meet so at least 11 stripes are needed.Using digits to represent colours 12345314251 is an example solution
  14. SubscriberPonderable
    chemist
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    28 Feb '22 10:441 edit
    @venda said
    A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
    What is the smallest number of stripes that it could have
    I suspect it's a bit like the map problem where each adjacent country had to be a different colour
    So I understand we need to design a flag made up of horizonatl stripes,in which we ensure that each colour has at least one neighbour with each colour.

    Reveal Hidden Content
    Evidently we need to have each colour more than once. If I replace the colour by number my first design is 12345.

    I add a 2 between 4 and 5 and get 123425. Now for 2 the condition is set. I can add a 1 between 3 and 4: 1231425 (I keep in mind that I want to make another 1 to neighbour to 5.
    If I add a 4 at the end and a 3 I get
    123142543 and have now 2 and 4 statisfied.

    with the addition of 5 and then1 I get
    12314254351

    That is eleven stripes. It is a solution, but maybe not the optimum. I can't get my head around for a formula, so I did it by hand 😉
  15. SubscriberPonderable
    chemist
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    28 Feb '22 10:46
    @venda said
    No. I didn't understand it either.I think the wording is a bit ambiguous.
    I'll post the given answer and explanation hidden
    Hidden content removed
    Seems that I got the wording right.
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