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Reducing 1 million to 7

  1. Jan 11, 2005 #1
    Can you reduce 1,000,000 to 7 using only the functions +,-,X and / with the digit 7?

    I know a lengthy way of doing it - [tex][1,000,000 - \frac{7}{7}] \div 7 \div 7 \div 7 ...[/tex].

    Is there a shorter way?
     
  2. jcsd
  3. Jan 11, 2005 #2
    [tex](1,000,000 - \frac{7}{7}) \div(7^7) \div(7^7)...[/tex]

    It is a bit shorter.

    The Bob (2004 ©)

    EDIT: [tex](1,000,000 - \frac{7}{7}) \div(7^7) = 1.2142645[/tex] That decimal run does not seem to have a fraction that can be put to it so I am stuck on how you got 7 from what you had.

    [tex][(1,000,000 - \frac{7}{7}) \div(7^7)]+[(7\times\frac{7}{7})-\frac{7}{7}]= 7.2142645[/tex] which is close.
     
    Last edited: Jan 11, 2005
  4. Jan 11, 2005 #3
    [tex]\left(\frac{77 - 7}{7}\right)^{(7 - \frac{7}{7})}[/tex]
     
    Last edited: Jan 11, 2005
  5. Jan 11, 2005 #4
    I forgot to mention that you're supposed to solve this by using a basic calculator that has no 'power' function. This renders the two solutions above to the realm of the 'lengthy'.
     
  6. Jan 11, 2005 #5
    [tex]\left(\frac{77 - 7}{7}\right)\left(\frac{77 - 7}{7}\right)\left(\frac{77 - 7}{7}\right)\left(\frac{77 - 7}{7}\right)\left(\frac{77 - 7}{7}\right)\left(\frac{77 - 7}{7}\right)[/tex]

    or

    [tex]\left(777 + 7 \times 77 - \left(7 + 7 + 7 + 7 + \frac{7}{7}\right)\right) \times 777 + \frac{7}{7}[/tex]

    or

    [tex]\frac{7,777,777 - 777,777}{7}[/tex]

    or even

    [tex]\frac{777777}{.777777}[/tex]
     
    Last edited: Jan 11, 2005
  7. Jan 11, 2005 #6
    Sorry ceptimus, but you've got to start out with the number 1,000,000 and then reduce this number to 7 using any one of the basic functions mentioned in my earlier post.
     
  8. Jan 11, 2005 #7
    [tex]1,000,000 \times \frac{.777777 \times 7}{777777} = 7[/tex]
     
  9. Jan 11, 2005 #8
    Sorry to disappoint you again. It seems that I have not explained the problem properly. Try to imagine that you're using a calculator that has only the buttons [tex]1,0,7,+,-,\div, \times, =[/tex]. You may only use the 1 and 0 buttons for inputing the number 1,000,000 and for nothing else.

    So you can now see that it is not possible to use decimal points the way you used it. :)
     
  10. Jan 11, 2005 #9
    :grumpy: How about

    [tex]1,000,000 \times (7 - 7) + 7 = 7[/tex]

    :tongue2:

    OK, that still uses brackets, and it's cheating.
     
  11. Jan 11, 2005 #10
    I like that! :rofl: However, I think that's cheating... o:)

    Then again, I also did cheat with the brackets in my first post.
     
  12. Jan 11, 2005 #11
    This works on a basic 4-function calculator without a decimal point.

    [tex]1,000,000\;-\;7\;\div\;7\;=\;\div\;777\;-\;7\;\times\;77\;+\;7\;+\;7\;+\;7\;+\;7\;+\;7\;\div\;7\;=\times\;7\;\div\;777\;=[/tex]
     
  13. Jan 11, 2005 #12

    Gokul43201

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    Did you mean :
    [tex]([1,000,000 - \frac{7}{7}] \div 7) - 7 - 7 ... ~~~?[/tex]
     
  14. Jan 11, 2005 #13

    Gokul43201

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    If you're allowed to hit the 1/X button (which you're not), there's an easy way :

    (1,000,000 + (777,777/7) )/7,777,777...and take the reciprocal.
     
  15. Jan 11, 2005 #14
    Actually, yes. But it still won't work. :mad:
     
  16. Jan 12, 2005 #15
    If you don't have to say 1,000,000 _first_, (7-7)*1000000 + 7 can be done on a basic calculator.
     
  17. Jan 12, 2005 #16
    Or, if you take advantage of the limited # of digits that can be stored in a basic calculator, you can do something like 1000000 / 7777777777777777 + 7
     
  18. Jan 12, 2005 #17
    I think this may be the hardest brain teaser, yet. :tongue:

    It looks so simple, though... :cry:
     
  19. Oct 29, 2005 #18

    meL

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    1000000 1001 /
     
  20. Oct 30, 2005 #19
    Very interesting question.

    1000000 - 777777 - 77777 (repeat twice) - 7777 (repeat 8 times) - 777 (five times) - 77 (seven times) - 7 (four times) *7

    would be one rather convoluted solution. I'm sure there's something better though, some number up there ought to be an even multiple of 7, 77, 777, etc. I'm seeing if I can find a more solid solution.
     
  21. Oct 30, 2005 #20
    Wow, I exahausive searched 7k, 77k, 777k.. with each other over +-10 and not a single number is divisible by 7 (or 77, 777 etc, though that would have been kind of a bounus). Unless I did it wrong (and it's entirely possible that I did) I can't find anything. There are several +- solutions that end up with 1 like the one I did above, like:
    1000000
    -777777
    -77777 (3x)
    +7777
    +777 (4x)
    +77 (3x)
    -7
    *7
    for instance. I'm not sure what's considered the "shortest", like fewest buttons pushed? I might do a more solid optimize if I have time or if someone else would enjoy it then go ahead.

    [EDIT] Doh.. Adding various multiples of 7 won't have much of an effect on divisibillity by 7, will it now? I'm still thinking about the posibillity of slight mods like *7+7/7 (i.e. +1) in strategic places though, that's probably the ticket if there is a trivial solution.
     
    Last edited: Oct 30, 2005
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