Brain teaser : The answer is 6.

[Guysanto]

Take each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 THREE TIMES AND ONLY THREE TIMES, such as (1, 1, 1), (4, 4, 4), (9, 9, 9). Use any mathematical operators you wish and apply to them to get the number 6, as the answer to your calculations.

Some of them are easy, some of them are hard, but there is an answer for any "triplet" of 1, 2, 3, 4, 5, 6, 7, 8, 9.

I'll start you off with a couple of easy ones:

2 + 2 + 2 ? The answer is 6.

6 + 6 - 6 ? The answer is 6.

All right, now try the others. It's not as easy as one might think, but it's not as hard as one might think either. Perhaps the hardest is the one with the 1's. You probably should leave it for last.

Guy

[Shelony]

3 x 3 - 3 = 6

Shelony

[Shelony]

another one that is not that hard

5/5 + 5 = 6

Shelony

[Shelony]

In the same line one could have

7 - (7/7) = 6

[Shelony]

Another one before I stop

[4-(4/4)]! = 6

Shelony

[Shelony]

I am sure I solve the last 3 (1, 8 and 9) but I let another person work them.

Shelony

[Anacaona]

Here is one

(1+1+1)!=6

Ana!

[Anacaona]

Here is another one

(sqrt(8/8 +8))! = 6

Finally
(sqrt(9+9-9))!=6

Sorry I cheated! Ana

[Guysanto]

Wow, wow, wow! Congratulations to Shelony and Anacaona, my factorial queens! {However, it's quite possible to find answers for 4, 8, and 9 without using factorials -- but I see that Anacaona is a big fan of factorials. That's probably why she signs her name as "Ana!" or "Anacaona!"}

I thought that (1, 1, 1) would be the hard one, but when Shelony put down

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[4 - (4/4)]! = 6

she opened the door wide for factorial-happy little sister. But since a number of people are either not familiar or have forgotten what they learned about factorials, permutations, and combinations (common operators in the field of probability and statistics) let me develop Shelony's and Ana's answers a bit more:

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[4 - (4/4)]! = [4 - 1]! = 3! = 3 x 2 x 1 = 6

Similarly,

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(sqrt(8/8 + 8))! = (sqrt(9))! = 3! = 3 x 2 x 1 = 6

and

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(sqrt(9 + 9 - 9))! = (sqrt(9))! = 3! = 3 x 2 x 1 = 6

[where "sqrt" stands for "square root" and "!" is the standard factorial sign]

and finally, my favorite:

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(1 + 1 + 1)! = 3! = 3 x 2 x 1 = 6

So, congratulations once more to Shelony and Anacaona who found ALL THE ANSWERS by the rules that I had set, but I would challenge Ana! to give us some non-factorial solutions for 4, 8, and 9 all the same.

Mezanmi, medam sa yo pa manje anyen'k frèt non nan zafè chif yo! Yo pap pran nan doub sis.

[Shelony]

Thank you Guy but now, you make it more difficult by asking answers without factorial. I have to confess that our mind works in weird way sometimes. I got the answer I put down for 4 long before I could think of something for 1. Anyway, I took the challenge to my husband last night and the first two he solved were 2 and 6 (he said 2 x 2 + 2 =6 and 6 x 6/6 = 6, big fan of multiplication), 5 and 7 soon followed. But I had to remind him that there was something called factorial and he solved the other ones as Ana and I did. But now I am thinking how can one possibly solve 4, 8, and 9 without the beloved factorial. I'll see what comes.

Shelony

[Shelony]

Now, this is what I can come up with

?(4) + ?(4) + ?(4) = 6 (I mean square root)

so,

?(9) x ?(9) - ? (9) = 6

and for 8 it could be

third root (8) + third root (8) + third root (8)= 2 + 2 + 2 = 6

Shelony

[Anacaona]

here is another way

9/sqrt(9) + 9 = 3 + 3 = 6

8/cubert( 8 ) + cubert ( 8 ) = 4+2 = 6

4/sqrt(4) + 4 = 2+4 = 6

Ana!

[Anacaona]

sorry I made a mistake.

I mean

9/sqrt(9) +sqrt(9) = 6

also 9 - 9/sqrt(9) = 6

Ana!

[Guysanto]

Shelony, those littles faces are just happy to see you! They were happy to see Ana! too, earlier and I had to tell them to refrain themselves.

That reminds me of the Mae West line: "Is that a gun in your pocket or are you just happy to see me?"

Seriously, you make a happy face whenever you write the number 8 immediately followed by the right parenthesis. There may be other combinations of numbers and symbols that will translate unintentionally to smilies (more aptly named EMOTICONS, since they are not all smiling or laughing). How can you prevent that? Well, you can check the option "Disable Smilies in this post" below the text box, before you submit your post.

Since I am a jack of all trades [I also play psychologist on occasion], I can see some differences of personality between the sisters. One writes "?", the other "sqrt" (or squirties). One writes "third root", the other writes "cubert" (or Qbert). I can see who is having more fun, can't you? No, not really, I am only joking. I am sure that Shelony has a ball sharing mathematical jokes with her husband, whenever Little Stephan allows them.

All right, I will be coming with more mathematical puzzles, now that I am assured that at least two people do not mind having fun on Ann Pale. And if you are not into math, well don't forget the "Krik! Krak!" section as well. Don't be intimidated by people who feel that you have to be serious all the time! I (seriously) believe that you are better equipped to help manage some of the world's biggest challenges if you preserve a sense of humor and are willing to use it to communicate with your peers and members of your communities.

[Shelony]

Since I am a jack of all trades [I also play psychologist on occasion], I can see some differences of personality between the sisters. One writes "?", the other "sqrt" (or squirties). One writes "third root", the other writes "cubert" (or Qbert). I can see who is having more fun, can't you? No, not really, I am only joking. I am sure that Shelony has a ball sharing mathematical jokes with her husband, whenever Little Stephan allows them.

These "differences of personality" are the result of not doing any real math since after college. All I do now are the four arithmetic operations and even them, I don't really do. My calculator does them. My sister had a good laugh when she saw my "third root".

Next time, I'll ask Stephan and Dad to check my answer before I post them for Ana to see.

Bay the way, Stephan is having fun singing and entertaining everyone with "rezistans o, si n pat gen rezistans n pa tap fete endepandans, woule tyatya". Mwen gen you ti patriot.

Shelony

[Morisseau]

Hey Guy, i like this one. I started working on it but my found answers were already posted...I am probably too slow. Keep coming with them brother.

[Guysanto]

O Morisseau, mwen tèlman sezi mwen pa kab ekri. Ou kwè se oumenm vre?

[Morisseau]

Yes sir! Listen, i religiously check the site several times a day. The problem is, I used not to have time to gather my thoughts for valuable comments as my contribution that I forget that I have enough time now to actively participate. I've been following. It is called "the quiet fan". Keep it up Guy, my classmates are using this site for their papers on Haiti.