# Many More Sixes

This is an ongoing riddle to see how far we can get as a group.

Similar to “Just One” we try and figure out how to use six 6’s to equal 1 (O.K. that’s been solved) then 2, then 3, then 4, etc. to see how far we can get.
We are to come up with answers in sequence (2, 3, 4, 5, etc.) and the same person is not allowed to produce two answers in a row. So if I come up with the solution for 2. I must wait until someone else posts a solution for six 6’s equaling 3 before I provide a solution for six sixes equaling 7. Etc.

How high can we get 6 sixes to go?

Thank you Brent for your great submission.
We will keep this one unsolved until the great computer tells us there is no greater answer, yet 42 is the answer to everything.

### 283 guesses to Many More Sixes

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• brent

Oh yeah, I think factorial is a great operation!
(6 x 6) + (6 x 6) + 6/6 = 73
“The best number is 73…. 73 is the twenty-first prime number. Its mirror, 37, is the twelfth and its mirror, 21, is the product of multiplying (hang on to your hats) 7 and 3…. In binary, 73 is a palindrome: 1-0-0-1-0-0-1, which backwards is 1-0-0-1-0-0-1.”

• Frank

6 * (6+6) + (6+6)/6 = 74

• Milan

6*6+6*6+6-6/2=75

• brent

Hi Milan, we are trying to use only math operations and six of the “6”. So it would be better not to include the “2” in your example. Maybe we could use something like:

6 x (6 + 6 + 6/(6 + 6) ) = 75

• Frank

(6 + (6/6)) x 6/.6 + 6 = 76

• brent

66 + 6/.6 + 6/6 = 77

• Frank

6 x (6+6) + 6 + 6 – 6 = 78

• brent

6 x (6 + 6) + 6 + 6/6 = 79

• Frank

6/.6 x (6+(6+6)/6) = 80

• brent

I’m torn on 81…
SQRT( SQRT(6 x .6 – .6) ^ (6/.6 +6) ) ) = 81
or
(6! x .6 – 6) / 6 + 6/.6 = 81

• Frank

(6×6)+(6×6)+6/.6 = 82

• brent

66 + 6 + 66/6 = 83

• Frank

6×6+6×6+6+6=84

• brent

( (6! x .6 + 6) / 6 ) + 6 + 6 = 85

• Frank

66+6/.6+6/.6=86

• brent

.6 X ( ( 6! + 6! ) x .6 + 6 ) / 6 = 87

• Frank

66 + 6/.6 + 6 + 6 = 88

• brent

( 66 – 6.6 – 6 ) / .6 = 89

• Frank

66+6+6+6+6=90

• brent

( 66.6 – 6 – 6 ) / .6 = 91

• Frank

6x(6+6) + (6+6)/.6 = 92

• brent

( ( 6! x .6 ) + ( 6! / 6 ) + 6 ) / 6 = 93

• Frank

66/.6 – 6/.6 -6 = 94

• brent

( 6/.6 + 6 ) x 6 – 6/6 = 95

• Frank

66 + (6-6/6)*6 = 96

• brent

( 6/.6 + 6 ) x 6 + 6/6 = 97

• Frank

6 x (6+6+6) – 6/.6 = 98

• brent

( 666 / 6 ) – 6 – 6 = 99

• Frank

(6/.6)x(6/.6) +6-6 = 100

• Crabman

I’m not sure that using 0.6 meets the criteria of the riddle. Also factorials seam to be cheating. 6! is just short hand for 6x5x4x3x2x1. As well a square root has an implied 2 in the function, just as the square of 6 does. Same with cube & cubed root has a 3 in the function

None of the above should be interpreted as me (who the heck am I anyway?) saying that the answers aren’t valid, and I really want to say that I applaud everyone’s ingenuity. I am just being pedantic :) Good job everyone.

• brent

Crabman you make good points! “square root” is kinda easy to write on paper as a common symbol but difficult to express on the computer. The other examples you give we may have just bent to rules too far as well, but given the convention we’ve been using, it’s still a lot of fun to try and find the next in the sequence every day or two.

Today’s answer I can submit without the shame of an implied ‘0’ or the factorial sign/operator:

6666/66 = 101

• Frank

(6-6/6)! – 6 -6 -6 = 102

• brent

66 + ( 6 x 6 ) + ( 6 / 6 ) = 103

• Frank

(6 -6/6)! – 6/.6 – 6 = 104

• brent

66/.6 – 6 + 6/6 = 105

• Frank

(6/.6 + 6) * 6 + 6/.6 = 106

• brent

( 6! – ( 6! / 6) + 6 ) / 6 + 6 = 107

• Amina

6×(6+6×6)=108

• Amina

6*(6 6 6)*(6/6)=108

• Amina

Argh!!
6×(6+6+6)×(6/6)=108

• brent

6 × ( 6 + 6 + 6 ) + ( 6/6 ) = 109

• Luca

(Of-topic) Hey Brent. While trying out different combinations. I discovered that any number multiplied by itself. Then the number divided by 11, squared.
Simply put:
X^2 /(X / 11)^2 = 121

While writing this down i also discovered that if you take 11 as y. Any y would lead to its square.
X^2 /(X / y)^2 = y^2

Isn’t that crazy!?
Or am i overseeing some simple algebra in this? (shame on me if i did xD)

• Luca

^^(Off-topic) sheesh…

• brent

Is x^2 / (x/y)^2
= x^2 / (x^2 / y^2)
Which is similar to A/(A/B) = A x B/A = B (to divide by a fraction, invert and multiply)
So x^2 / (x^2 / y^2) = x^2 x y^2 / x^2 = (x^2 x y^2) / x^2 = y^2

• Luca

Thanks, Brent for clarifying. As i can see i have obviously overseen such simple algebra xC.
Well, i guess i’ll start studying again! xD.

• Frank

666/6 – 6/6 = 110

• brent

( 6! – 6 – 6 – 6 ) / 6 – 6 = 111

• Frank

(6/.6)x(6/.6) +6+6 = 100

• Frank

OOPS = 112

(6/.6)x(6/.6) +6+6 = 112

• brent

66 / .6 + ( 6 x .6 ) – .6 = 113