On Friday I posted this puzzle:

How can you express the number 100 using six nines and no other digits?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

99 99/99

Did you solve it? Any other solutions?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle **(UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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Wait.. what? Shouldn’t there be a plus between the first two ’99’s?

(999-99)/9

99/9 * 9 + 9/9

That’s what I came up with on Friday.

I think there’s a plus sign missing in Richard’s solution

and I’m now awaiting all the other solutions.

I also had 99.9999 (recurring)

and 99+99/99 and (9/9)*(9/9)+99

and I know there were some [other] good ones

“I also had 99.9999 (recurring)”

The proper notation requires only 3 digits (if this blog supports it): 99.9̅

You forgot the plus! What a fail.

1¼

(9 * 9) + 9 + 9 + 9/9

This is what I went with too.

that was mine, witch I find cooler, as each 9 is used as a single number.

I did this one as well.

Lord Manley,

Great to hear that you went with that one. Are you now in a position to elaborate on your two answers to Richard’s puzzle of 6th December when you commented “I have one which requires capitals and one which does not.”?

I got 9*9+9+9+9/9

(Ed was quicker)

No plus sign missing, it is an expression of a single number: ninety-nine and ninety-nine ninety-ninths, not 99+99/99. Simply a limitation of the medium.

Good call. And it means that everyone who did use +*/- etc were wrong. Double win.

Except Richard has now added in the plus sign

I don’t see a plus sign in Richard’s piece at the top. It doesn’t make those that used + or * wrong, it is simply another answer.

Without some sort of designation/operator they would be read as two separate numbers, 99 and 1.

I would argue that a mixed number is not properly formed unless the fractional part is strictly less than 1.

11 using only +, —, * and /

99+(99/99)=100 <This was my almost instantaneous answer

(9+9/9)*(9+9/9)=100

(9*9)+9+9+(9/9)=100

99-9+9+(9/9)=100

99*(9/9)+(9/9)=100

[99+(9/9)]*(9/9)=100

99+(9*9)/(9*9)=100

(99+9/9)+(9-9)=100

(99/9)*9+(9/9)=100

(99+9/9)/(9/9)=100

(999-99)/9=100

Plus another 17 using √ and ^

99+(9^9/9^9)=100 (i.e. 99+99/99)

(9+√9/√9)*(9+9/9)=100

(9+√9/√9)*(9+√9/√9)=100

(9*9)+9+9+(√9/√9)=100

99-9+9+(√9/√9)=100

99+(√99/√99)=100

99*(√9/√9)+(9/9)=100

99*(9/9)+(√9/√9)=100

99*(√9/√9)+(√9/√9)=100

[99+(√9/√9)]*(9/9)=100

[99+(9/9)]*(√9/√9)=100

[99+(√9/√9)]*(√9/√9)=100

(99+√9/√9)+(9-9)=100

(99/9)*9+(√9/√9)=100

(99+√9/√9)/(9/9)=100

(99+9/9)/(√9/√9)=100

(99+√9/√9)/(√9/√9)=100

99+[cos(tan(sin(9)))*e^(sin(√9))]/[cos(tan(sin(9)))*e^(sin(√9))]

(9×9)+9+9+9/9

999/9.99

The coolest answer in my opinion 🙂

99 + (99^(9-9)) = 100

(9×9)+9+9+(9/9)

(999 – 99) / 9

999999 in Copeland-Bois base = 100

Understand the problem? I don’t even understand the solutions.

As I suspected. Another nice one!

I mis-red it, so used the number 9 rather than the digit:

(9×9) + (9+9) + (9/9)

Can anyone offer the solution with five nines instead, as mentioned on Friday?

I had a lot of answers. One of the answers is:

99+99^(9/9)

And that one works with 5 or more 9s. 99+9^(9/9) or 99+999^(9/9) etc.

Sorry… I mean 99+99^(9-9)

and 99 + 9^(9-9)

I’m genuinely surprised to say that I understand that, Geodetective! I didn’t think I’d ever remember GCSE And A Level Maths! Thanks.

99+9/(√9√9) – I’m sure you’re not going to like the use of ‘√’ though.

NOON in 1.42857 secs

999/999%

1%?

I’m shocked by how many ways there are for doing this. And I’m showing it to my grandchildren who are both very shocked and surprised.

99+99/99

99+99/99

I can do it in 3: 99.(9)

Oh wow, i feel stupid now.