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HALLOWEEN Puzzle answers

Discussion in 'Welcome lounge and forum help' started by YouMakeMeBlush, Oct 31, 2008.

  1. 1. Ans = Molly reasoned that the number of digits in 2 to the power of n plus the number in 5 to the power of n is the same as in 10 to the power of n, namely n + 1. [e.g. the number of digits in 2 is 1; in 5 is 1. 1 + 1 = 2 = the number of digits in 2 x 5 (=10) = 2. The number of digits in 2 to the power of 4 is 2, and in 5 to the power of 4 is 3, and that in 10 to the power of 4 is 5. The number in 2 to the power of 2008 + the number in 5 to the power of 2008 is equal to 2009. So given the number of digits in 2 to the power of 2008, Molly finds by subtraction from 2009 the number of digits in 5 to the power of 2008.]


    2. Ans = The short answer is "tired". On the other hand the pattern 4 x 4 = 16, 4 x 44 = 176, and 4 x 444 = 1776, means that we can write down the answer without writing out the sum. Since 4 x 4 = 16 (6 with a carry of 1), the last digit is 6, and every other digit apart from the first must be 6 + 1 = 7. The first digit will be the carry of 1. So the answer must be 1[7]6 where [7] is a string of (n - 1) 7s, where n is the number of 4s in the string of 4s being quadrupled. In this case we have 4444 4s, so the answer is the number formed by writing down 1 followed by 4443 7s and a single 6.


    3. Ans = King is two-thirds of Knight (no. of letters)
     
  2. 1. Ans = Molly reasoned that the number of digits in 2 to the power of n plus the number in 5 to the power of n is the same as in 10 to the power of n, namely n + 1. [e.g. the number of digits in 2 is 1; in 5 is 1. 1 + 1 = 2 = the number of digits in 2 x 5 (=10) = 2. The number of digits in 2 to the power of 4 is 2, and in 5 to the power of 4 is 3, and that in 10 to the power of 4 is 5. The number in 2 to the power of 2008 + the number in 5 to the power of 2008 is equal to 2009. So given the number of digits in 2 to the power of 2008, Molly finds by subtraction from 2009 the number of digits in 5 to the power of 2008.]


    2. Ans = The short answer is "tired". On the other hand the pattern 4 x 4 = 16, 4 x 44 = 176, and 4 x 444 = 1776, means that we can write down the answer without writing out the sum. Since 4 x 4 = 16 (6 with a carry of 1), the last digit is 6, and every other digit apart from the first must be 6 + 1 = 7. The first digit will be the carry of 1. So the answer must be 1[7]6 where [7] is a string of (n - 1) 7s, where n is the number of 4s in the string of 4s being quadrupled. In this case we have 4444 4s, so the answer is the number formed by writing down 1 followed by 4443 7s and a single 6.


    3. Ans = King is two-thirds of Knight (no. of letters)
     
  3. 4. Ans = GROOM


    5. Ans = REFEREE


    6. Ans = COASTLINE


    7. Ans = If there were any logic in these things, 4th (put on a pair of glasses that sees only Roman numerals). Mind you, an alternative explanation could be that the trainer called the horse from the stable with the arch words, "come forth".
     
  4. 8. Ans = 576 (there was a long expl. with it, but surely you can work this one back and prove it true.)


    9. Ans = SCHOONER


    10. Ans = Nothing
     
  5. MISSING (YO)U
     
  6. 12. Snobbery
     
  7. DM

    DM New commenter

    I spent 20 minutes figuring out the answers to 1) and 2) and expected to receive great acclaim for posting the solutions only to find myself redundant and usurped by the question setter.

    [:'(]
     
  8. DM

    DM New commenter

    Oh ... and your smiley's are broken!
     
  9. DM

    DM New commenter

    smileys
     
  10. DM

    DM New commenter

    It wasn't a total waste of time.

    I now know there are 605 digits in 2 to the power of 2008.
     
  11. DM

    DM New commenter

    As people connected with the TES are reading this thread, can I post a request.

    Would it be possible to add LaTeX to the site? It is completely free for you to do so and means we can typeset mathematics properly. I think it would do a lot to increase activity on the mathematics forum in particular.
    http://community.tes.co.uk/forums/t/257910.aspx
     
  12. 13. Ans = If you take SEVEN (odd) and delete the first letter, you make it EVEN. It says "character" and not "digit."


    DM: I don't know if TES are bothering to read this innocuous thread. And I'm not TES, honest. I suggest you email your message to help@tes.co.uk
     
  13. DM

    DM New commenter

    13. Cutting off the first character of this odd number makes it even. Which and how?

    There are any number of answers if you work in roman numerals.

    III is odd II is even

    IX is odd X is even


     
  14. DM

    DM New commenter

    Cute Vamp,

    I thought you were TES! It says you are in the little logo over your shoulder.
     
  15. [:'(] - Yes the smileys are broken. Where's the real Harminder?
     
  16. DM

    DM New commenter

    I should have read your little message at the bottom.
     
  17. Yes it does say TES over our shoulders . . . erm . . . so enjoy our avatars while you can . . .
     
  18. 14. Ans = RESPIRATION
     
  19. 15. Ans = Boudicca, Coriolanus, Acceleratus.
     
  20. 16. "Up to and Including 10 Items." ("10 Items or Fewer" is never used, for some reason). The number 55371 on a calculator just about reads "1 LESS" when seen upside down.
     

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