Edit: A commenter below found a real answer. I was really wrong this time. Sorry. I guess I should delete my embarassing remarks, but better to let them stand as a reminder to me.

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Further edit: My error now seems obvious. My initial approach assumed that the first step would be to combine two numbers (this was correct) leaving a new 24 puzzle with 3 numbers. Good. But then I tried all ways to combine 3 and 3, then 8 and 8, then 3 and 8. I was ok with 3 and 3 and 8 and 8, but when I looked at 3 and 8 I excluded 8/3. Why? I wasn't looking for a fraction on the way to a whole number answer. Sloppy.

Thanks to Eric C for correcting me (below)
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K, since I wrote Monday that in the game of 24 {3,3,8,8} has no solution, I have seen a surge (as much of a surge as you might see if you had a blog with 1 – 2 dozen search engine hits per day) in searches related to this puzzle.

There is a solution. It is illegal. It involves using a decimal, and a line over a decimal. .8 with a bar over the 8…

_
.8

Maybe that is what it looks like. Anyway, 3*[8 / (.8-bar)] – 3 = 24.
.8-bar = 8/9.
8 divided by 8/9 = 9
9*3 = 27
and 27 – 3 = 24

It's illegal. Can't be done legally. You can stop looking now.

June 2, 2006 pm30 6:32 pm 6:32 pm

I found this solution posted on another site.

8 / (3 – 8/3)

July 8, 2008 pm31 1:16 pm 1:16 pm

i have a lot of time to this prob..

goodluck..

December 2, 2010 am31 12:51 am 12:51 am

This is the Answer 8 /3 = 2.666666666666667
2.666666666666667 – 3 = .3333333333333333
.3333333333333333 / 8 = 24

This is Sooooo Easy why do people have trouble with this
Tip* be careful what calculator
By Nylegend 516

December 2, 2010 am31 1:07 am 1:07 am

Switch the #s
This is the Answer 8 /3 = 2.666666666666667
3 – 2.666666666666667 = .3333333333333333
8 / .3333333333333333 = 24

This is Sooooo Easy why do people have trouble with this
Tip* be careful what calculator
By Nylegend 516

October 5, 2011 pm31 4:43 pm 4:43 pm

My young 11 year old nephew came up with the following solution.
24 = the square root of 8 times 8 multiplied by the square root of 3 times 3

December 2, 2010 am31 1:04 am 1:04 am

Switch the #s
This is the Answer 8 /3 = 2.666666666666667
3 – 2.666666666666667 = .3333333333333333
8 / .3333333333333333 = 24

This is Sooooo Easy why do people have trouble with this
Tip* be careful what calculator
By Nylegend 516

December 2, 2010 am31 1:06 am 1:06 am

Switch the #s
This is the Answer 8 /3 = 2.666666666666667
3 – 2.666666666666667 = .3333333333333333
8 / .3333333333333333 = 24

This is Sooooo Easy why do people have trouble with this
Tip* be careful what calculator
By Nylegend 516

December 13, 2011 am31 3:57 am 3:57 am

the solution is 8/3-(8/3) =24

6. February 10, 2012 am29 3:33 am 3:33 am

I have no idea what those mean but on the sheet of paper
It says that you are only allowed to use plus,multiply,divide and take away