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.

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

1. Anonymous says:

(999-99)/9

1. Navneeth says:

That’s what I came up with on Friday.

2. ChrisR says:

I think there’s a plus sign missing in Richard’s solution
and I’m now awaiting all the other solutions.

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

and I know there were some [other] good ones

1. “I also had 99.9999 (recurring)”

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

3. Baker's Dozen says:

You forgot the plus! What a fail.

1. Eddie says:

4. Ed Wilson says:

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

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

2. Effete Serf says:

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.”?

5. Julia says:

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

1. Julia says:

(Ed was quicker)

6. Chris says:

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.

1. Bryan says:

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

2. ChrisR says:

Except Richard has now added in the plus sign

3. Chris says:

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.

4. Anonymous says:

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

5. ivan says:

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

7. I Claudius says:

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

8. Eddie says:

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

9. Anita Evans says:

(9×9)+9+9+9/9

10. neil says:

999/9.99

11. Alex says:

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

12. Jarty says:

(999 – 99) / 9

13. Dave says:

999999 in Copeland-Bois base = 100

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

15. As I suspected. Another nice one!

16. michael says:

I mis-red it, so used the number 9 rather than the digit:
(9×9) + (9+9) + (9/9)

17. Anne Elk says:

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

99+99^(9/9)

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

2. Sorry… I mean 99+99^(9-9)
and 99 + 9^(9-9)

3. Anne Elk says:

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.

18. Eddie says:

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

19. Lazy T says:

NOON in 1.42857 secs

20. Alan S says:

999/999%

1. Anon says:

1%?

21. 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.

22. Anonymous says:

99+99/99

23. Tanja henney says:

99+99/99

24. slw says:

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

25. Anonymous says:

Oh wow, i feel stupid now.