## 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.

July 5th, 2011 at 3:49 pm

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.

July 5th, 2011 at 4:13 pm

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

July 5th, 2011 at 4:17 pm

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.

July 5th, 2011 at 4:20 pm

2=1*(9-9)+2

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

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

This is what Chandler proposes

July 5th, 2011 at 7:34 pm

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

July 5th, 2011 at 8:24 pm

@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…)

July 5th, 2011 at 10:55 pm

@Chris: Psych! I was just kidding about the “10=” XD. Here’s the REAL answer.

10=(1^9)+(sqrt(9)^2)

July 6th, 2011 at 1:03 am

Lol at claiming your mistake was a joke.

July 6th, 2011 at 1:05 am

…..

100=1+9*(9+2)

aaaaaaaaaand im done, youll just have to trust me on the other 99.

July 6th, 2011 at 1:13 am

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)

July 6th, 2011 at 3:15 am

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)

July 6th, 2011 at 3:18 am

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.

July 6th, 2011 at 4:53 am

Good find Chris

July 6th, 2011 at 5:33 am

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

July 6th, 2011 at 5:37 am

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

July 6th, 2011 at 5:53 am

93=1^9+92

July 6th, 2011 at 5:56 am

really sick if they are only solvable by “gluing”

July 6th, 2011 at 7:34 am

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

July 6th, 2011 at 7:58 am

Good work all.

97 = 1 * 99 – 2

July 6th, 2011 at 8:10 am

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

July 6th, 2011 at 8:55 am

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?

July 6th, 2011 at 12:32 pm

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

July 8th, 2011 at 3:21 am

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!

July 8th, 2011 at 6:40 am

That’s not cheating, it is innovative.

July 10th, 2011 at 2:02 am

Thanks John24!

July 10th, 2011 at 2:52 am

If 9/.2 can be used, then:

95=(1+9+9)/.2

So then, 4 more remaining (68,93,94,97)

July 10th, 2011 at 3:10 am

Also,

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

which leaves 93,94,97