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1 Equals… (yep, different from the previous question…)

Posted by Karl Sharman on July 5, 2011 – 1:50 pm

1 = -1+9-9+2.

Extend this list from 2 through to 100 on the left side of the equals sign. +,-,/,x,(),sqrt,^,factorial(!) are all welcome in this exercise…. but…. the formula must use the four numbers in order 1 9 9 2.

Why??? I hear you ask – because the puzzle was originally written in 1992.

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  1. 1. Joey Said:

    2=(1+9-9)*2
    3=1+9-9+2
    4=1+(9/9)+2

    More later, this is all I have time for now.

  2. 2. Karl Sharman Said:

    By my calculations Joey, only 96 to go…..

  3. 3. Joey Said:

    5=((1^9)+9)/2
    6=-(1^9)+9-2
    7=(1^9)*(9-2)
    8=((1^9)+9)-2
    9=1+sqrt(9)+sqrt(9)+2
    10=1*(9+9+2)

    Well, that took long enough. That’s all I’m game for. Good luck with the rest haha.

  4. 4. slavy Said:

    2=1*(9-9)+2
    3=1+sqrt(9)-sqrt(9)+2
    4=1*sqrt(9)+sqrt(9)-2

    This is what Chandler proposes :P

  5. 5. Chris Said:

    6 = 2 * sqrt(9) * 1^9, sorry Joey, your 6 is 8
    10 = 9 + 1^(9+2), sorry Joey, your 10 is 20
    11 = (1^9)(2+9)
    12 = (1^9) + 2 + 9
    13 = sqrt(9) + 9 + 2 -1
    14 = 2(sqrt(9) + sqrt(9) + 1)
    15 = sqrt(9^1) (sqrt(9) + 2)
    16 = (sqrt(9) + 1^9)^2
    17 = (9 + 9 – 1^2)
    18 = (9 + 9) * 1^2
    19 = 9 + 9 + 1^2
    20 = 9 + 9 + 2^1

    ‘night all

  6. 6. Bekki Said:

    @Chris: Joey’s 6 is not an 8. I think you missed the – in the very front when you were looking at it. And, all of yours are invalid since the numbers have to go in order 1 9 9 2 (although I suppose you could fix some of them…)

  7. 7. Joey Said:

    @Chris: Psych! I was just kidding about the “10=” XD. Here’s the REAL answer.
    10=(1^9)+(sqrt(9)^2)

  8. 8. Jan Said:

    Lol at claiming your mistake was a joke.

  9. 9. Jan Said:

    …..
    100=1+9*(9+2)
    aaaaaaaaaand im done, youll just have to trust me on the other 99.

  10. 10. slavy Said:

    Hi Chris, you are not keeping the order of the digits, as Karl specifically asked. So some of your numbers fail to work. 6 is OK (after trivial reordering), but 10 is not. Let me try to rewrite/improve your answers:

    6=1^9*sqrt(9)*2
    10=1+9^(sqrt(9)-2)
    11=(1^9)*(9+2)
    12 = (1^9)+ 9 + 2
    13 = -1 + sqrt(9) + 9 + 2
    14 = (1 + sqrt(9) + sqrt(9))2
    15 = 1*sqrt(9)*(sqrt(9) + 2)
    16 = (1^9+sqrt(9))^2
    17 = -1 + 9 + sqrt(9)^2
    18 = 1*(9 + sqrt(9)^2)
    19 = 1 + 9 + sqrt(9)^2
    20 = 1*(9+9+2)

  11. 11. Jan Said:

    ok I gave it a serious try, still missing 7

    1=-1*(9/9)+2
    2=1*(9/9)*2
    3=1*(9/9)+2
    4=(1+9/9)*2
    5=-1+(9/sqrt(9))*2
    6=(1*9/sqrt(9))*2
    7=1+(9/sqrt(9))*2
    8=-1+(9+9)/2
    9=(1*9+9)/2
    10=1+(9+9)/2
    11=(1^9)*9+2
    12=1*(sqrt(9)+sqrt(9))*2
    13=1+(sqrt(9)+sqrt(9))*2
    14=1*sqrt(9)+9+2
    15=1+sqrt(9)+9+2
    16=1*(9+9)-2
    17=1+9+9-2
    18=(1^9)*9*2
    19=-1+9+9+2
    20=1*(9+9+2)
    21=1+9+9+2
    22=1+sqrt(9)+9*2
    23=(1+sqrt(9))!-sqrt(9)+2
    24=(1+sqrt(9))!*(sqrt(9)-2)
    25=(1+sqrt(9))!+sqrt(9)-2
    26=1+sqrt(9)*9-2
    27=1*sqrt(9)*(sqrt(9)^2)
    28=(1+9)*sqrt(9)-2
    29=1*sqrt(9)*9+2
    30=1+sqrt(9)*9+2
    31=(1+sqrt(9))!+9-2
    32=(1+9)*sqrt(9)+2
    33=-1+sqrt(9)!*sqrt(9)!-2
    34=1*sqrt(9)!*sqrt(9)!-2
    35=-1+(9+9)*2
    36=1*(9+9)*2
    37=1+(9+9)*2
    38=1*sqrt(9)!*sqrt(9)!+2
    39=1+sqrt(9)!*sqrt(9)!+2
    40=(-1+9*9)/2
    41=(1+9*9)/2
    42=(1+sqrt(9))!+9*2
    43=1+sqrt(9)!*(9-2)
    44=(1+sqrt(9))*(9+2)
    45=(1+9)*9/2
    46=(-1+9)*sqrt(9)!-2
    47=(-1+sqrt(9)!)*9+2
    48=(-1+9)*sqrt(9)*2
    49=(1+sqrt(9)+sqrt(9))^2
    50=(1+9)*(sqrt(9)+2)
    51=-1+sqrt(9)!*9-2
    52=1*sqrt(9)!*9-2
    53=-1+sqrt(9)*9*2
    54=1*sqrt(9)*9*2
    55=1+sqrt(9)*9*2
    56=(-1+9)*(9-2)
    57=-(1+sqrt(9))!+9^2
    58=(1+9)*sqrt(9)!-2
    59=
    60=((1+sqrt(9))!+sqrt(9)!)*2
    61=(1+sqrt(9)!)*9-2
    62=(1+sqrt(9))^sqrt(9)-2
    63=1*9*(9-2)
    64=(-1+sqrt(9)*sqrt(9))^2
    65=(1+sqrt(9)!)*9+2
    66=(1+sqrt(9))^sqrt(9)+2
    67=1+sqrt(9)!*(9+2)
    68=
    69=
    70=(1+sqrt(9))!*sqrt(9)-2
    71=-1+sqrt(9)!*sqrt(9)!*2
    72=(1+sqrt(9))!*sqrt(9)!/2
    73=1+sqrt(9)!*sqrt(9)!*2
    74=(1+sqrt(9))!*sqrt(9)+2
    75=-1*sqrt(9)!+9^2
    76=1-sqrt(9)!+9^2
    77=(1+sqrt(9)!)*(9+2)
    78=-1+9*9-2
    79=1*9*9-2
    80=1+9*9-2
    81=(1^9)*(9^2)
    82=-1+9*9+2
    83=1*9*9+2
    84=1+9*9+2
    85=1+sqrt(9)+9^2
    86=-1+sqrt(9)!+9^2
    87=1*sqrt(9)!+9^2
    88=(1+9)*9-2
    89=-1+9+9^2
    90=1*9+9^2
    91=1+9+9^2
    92=(1+9)*9+2
    93=
    94=
    95=
    96=(-1+9)*sqrt(9)!*2
    97=
    98=-1+9*(9+2)
    99=1*9*(9+2)
    100=1+9*(9+2)

  12. 12. Chris Said:

    Hi slavy. Thanks, I hadn’t noticed that rule.

    21 = 1 + 9 + 9 + 2

    Hi Bekki & Joey. My bad, Joe’s 6 is a 6 after all.

  13. 13. Jan Said:

    Good find Chris

  14. 14. slavy Said:

    Hi Jan, congratulations for the impressive job! I admit I am not very good at that so I won’t try very hard on the problem. However, Karl mentioned in the other problem (Equals 1) that here “gluing” is allowed. I don’t know if it is necessary (so far you haven’t used it and there are only 7 numbers left), but it makes life much easier. For instance

    59=19*sqrt(9)+2
    94=-1+sqrt(9)+92
    95=1*sqrt(9)+92
    97=-1+sqrt(9)!+92

  15. 15. slavy Said:

    68=-(1+sqrt(9))!+92

  16. 16. slavy Said:

    93=1^9+92

  17. 17. Jan Said:

    really sick if they are only solvable by “gluing”

  18. 18. Karl Sharman Said:

    I’ve only allowed gluing because I cannot solve 93, 94,95 & 97 without gluing… yet!

  19. 19. John24 Said:

    Good work all.

    97 = 1 * 99 – 2

  20. 20. Jan Said:

    but you did find 59, 68 and 69 the regular way?

  21. 21. slavy Said:

    59=-1+(sqrt(9)!)!/(sqrt(9)!*2)

    However 69 is killing me so far :( Just a question to Karl – is it allowed to use multiple factorials, e.g., 4!!=2*4?

  22. 22. Karl Sharman Said:

    Not on that side of the equation Slavy!

    Jan – I am away from home for a few days so I don’t have my ‘homework’ with me to refer to – I’ll let you know on Friday! Sorry to make to sweat a little longer ;-)

  23. 23. Karl Sharman Said:

    For 69 – I cheated – the shame….

    69= (1+sqrt(9))!+(9/.2)

    The rest, I have used “gluing”

    93= 1^9+92
    94= -1+sqrt(9)+92
    95= 19*(sqrt(9)+2)
    97= 1*99-2

    So a mere 5 more to go – the original answer in 1992 used 20 examples of gluing to complete the set. So, the ToM collective (mainly Jan) is way ahead of the class of ‘92!

  24. 24. John24 Said:

    That’s not cheating, it is innovative.

  25. 25. Karl Sharman Said:

    Thanks John24!

  26. 26. Ankit Said:

    If 9/.2 can be used, then:
    95=(1+9+9)/.2
    So then, 4 more remaining (68,93,94,97)

  27. 27. Ankit Said:

    Also,
    68=.1*(sqrt(9)!)!-sqrt(9)!+2

    which leaves 93,94,97

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