1. Subscribervenda
    Dave
    S.Yorks.England
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    12 Jul '21 14:00
    This weeks puzzle is(yet another) that i don't know how to do without resorting to trial and error:-
    700 stalls were in a row at a festival and each saw one more visitor than the previous.Each stall wrote down it's attendance and the 700 cards were passed to the auditor,who lost one.The auditor totalled the remaining cards as 700,000.
    What number went missing
  2. Standard memberAnitya
    Shoshin
    under a fig tree
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    12 Jul '21 23:54
  3. Joined
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    13 Jul '21 06:192 edits

    Removed by poster

  4. Joined
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    13 Jul '21 06:231 edit
    I recognized it as an arithmetic progression (AP) with a common difference of 1.
    A term in an AP has the for a + (n-1)d where a is the first term, n is the number of terms and d is the common difference.
    So the term is a+699.
    The sum of an AP is S(n) = (n/2){2a+(n-1)d}. So the sum is S(700) = (700/2){2a+699}. This simplifies to S(700)= 700a+244650.

    Call the missing card m. The mth term would be a+(m-1).
    The auditor found the total 700a+244650 -[a+(m-1)]=700000.
    700a+244650 -[a+(m-1)]=700000
    699a+244651-m=700000
    699a-m=455349
    Make a the subect of the formula
    a=(455349+m)/699
    The numbers a and m are counting numbers.
    Divide 455349 by 699 to get a number q and a remainder r. So
    q +r/699 +m/699 would be a.
    699=r+m and a=q+1. So you get m by finding 699-r.
    q=651 and r =300
    m=699-300=399
    a=651+1=652
    Card number 399 is missing.

    Checking the answer
    The sum is S(700)=700(352)+244650=701050
    The mth term is 652+398=1050
    The auditor's total is 701050-1050=700000

    So card number 399 is missing.
  5. Subscribervenda
    Dave
    S.Yorks.England
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    13 Jul '21 08:16
    @anitya said
    [hidden]350[/hidden]
    Incorrect I'm afraid
  6. Subscribervenda
    Dave
    S.Yorks.England
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    13 Jul '21 08:19
    @damionhonegan
    Correct and you've even taken it a stage further than the question which only gives the answer as the number of stall visitors missing!(1050)
    Well done
  7. Standard memberAnitya
    Shoshin
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    14 Jul '21 00:07
    @venda said
    Incorrect I'm afraid
    ah well
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    14 Jul '21 14:15
    @damionhonegan

    How did you calculate q?
  9. Joined
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    16 Jul '21 01:45
    @Eladar

    455349÷699= 651 with a remainder of 300. I called the remainder r. I made q be the quotient without the remainder.
  10. Joined
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    16 Jul '21 01:561 edit
    @damionhonegan

    Ok, got it now. I was missing that d=1, therefore simplifies out in both the nth term and adding in the mth term.

    Thanks
  11. Subscriberrookie54
    free tazer tickles..
    wildly content...
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    23 Jul '21 16:31
    i don't have the brainpower


    https://fivethirtyeight.com/features/can-you-hop-across-the-chessboard/
  12. Joined
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    14 Aug '21 00:17
    @rookie54
    Did you solve it?
  13. SubscriberBigDogg
    Father Mocker
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    14 Aug '21 16:40
    @rookie54 said
    i don't have the brainpower


    https://fivethirtyeight.com/features/can-you-hop-across-the-chessboard/
    I traced backwards from a King.

    Reveal Hidden Content
    e3, e4, d4, c5, b6, c7, a8
  14. Joined
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    09 Oct '21 06:53
    Do you have any more newspaper puzzles?
  15. Subscribervenda
    Dave
    S.Yorks.England
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    17 Oct '21 11:57
    @damionhonegan said
    Do you have any more newspaper puzzles?
    I do look every week but most of them are not very good so I don't bother posting them.
    This weeks is not very challenging but here goes:-
    I have a square.I increase the length of each side by 14 metres and it's area grows by 700 square metres(there's always a 700 element to them!!)What is the area of my new larger square
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