Two sides to the equation. On the right side you have to get answers from 1 through to 12.

On the left side of the equation the number 2 must be there 3 times, not more of not less. You can use any mathematical symbol you like but the 2 must be there 3 times. If you want to head into deep maths or stuff about with Access or Excel you are on the wrong tack.

A couple of obvious ones

2 + 2 + 2 = 6
2 X 2 X 2 = 8

Again the numeral 2 must appear 3 times on the left and get answers from 1 through to 12. I first saw this problem in the early 1970s and I have only seen one person solve it and he is a dentist. I have put it in a couple data base forums Access/SQL Server etc but no one has got the 12. It has been shown to engineers, medical specialists, maths teachers but so far only the dentist got the 12 done.

Only the number 2 can be on the left and again, it must be there 3 times.

2 + 2 + 2 = 6
2 X 2 X 2 = 8


2 -2 + 2 = 2

2^4 /2^3 + 2 = 4

2^0 + 2^0 + 2^0 = 3

2^3 / 2 + 2^0 = 5

2^3 - (2^-1 + 2^-1) = 7

2^3 + 2^-1 + 2^-1 = 9

2^3 + 2 + 2 = 12

2^3 + 2^0 + 2 = 11

2^3 + 2^0 + 2^0 = 10

2^2 / 2 - 2^0 = 1

quote:

Originally posted by 4sixteen:
2 + 2 + 2 = 6
2 X 2 X 2 = 8


2 -2 + 2 = 2

2^4 /2^3 + 2 = 4

2^0 + 2^0 + 2^0 = 3

2^3 / 2 + 2^0 = 5

2^3 - (2^-1 + 2^-1) = 7

2^3 + 2^-1 + 2^-1 = 9

2^3 + 2 + 2 = 12

2^3 + 2^0 + 2 = 11

2^3 + 2^0 + 2^0 = 10

2^2 / 2 - 2^0 = 1

First problem, you can only have 2s on the left side and you have 3s and a 4

Also brackets are important so 2 -2 + 2 = 2 would be (2-2) + 2 = 2

A good first attempt. I will give one clue. Some of the answers are much more easily obtained than you think.

2^3 + 2 + 2 = 12 Another one for brackets as in ((2^3) +2) + 2

For those not familiar with ^ it is raising a number to a power so 5^2 = 25 and 5^3 = 125

Also, check Windows Character as will make it easier for others to follow.

Again, NOTHING but 2s on the left and there must be three of them. That is why it got called the Three 2s problem.

Mister Jines with his connections will be along soon with the 12

I move that Mike McGuire be banned.

You inadvertently omitted 'base' number 2 in the problem definition. For my correct solution the base number 2 does in fact appear exactly 3 times.

Cryptozoologists rule.

quote:

Originally posted by 4sixteen:
You inadvertently omitted 'base' number 2 in the problem definition. For my correct solution the base number 2 does in fact appear exactly 3 times.

Cryptozoologists rule.

But also have a 3.

So a 2 must appear three times on the left side and no other number

quote:

Originally posted by Kensco:
I move that Mike McGuire be banned.

Take it up with Saeed.

Good luck

quote:

Originally posted by Mike McGuire:

quote:

Originally posted by 4sixteen:
You inadvertently omitted 'base' number 2 in the problem definition. For my correct solution the base number 2 does in fact appear exactly 3 times.

Cryptozoologists rule.

But also have a 3.

So a 2 must appear three times on the left side and no other number

Got it, but I'm not going to spoil the ending...

quote:

Originally posted by TomP:

Got it, but I'm not going to spoil the ending...

And you always have three 2s, not more not less on one side?

So 2/2 = 1 would not qualify.

If you have got it then you are the second person I have seen do it since about 1970.

When I first saw it I could not do it and the person who gave it to me did not have the answers.

In my little world I have to ask - who cares ?

quote:

In my little world I have to ask - who cares ?

Finally, someone added a dose of reality!!!!!

I have to agree that this is an abstract puzzle along the lines of the "Feducci Principle",(that of consentrict #'s equaling a whole).Never mind,look it up if you're interested. Myself,since I am in the s/m business I use geometry every day so I find math interesting.But that's just me.

It requires a lot of lateral thinking.

Yes it does;+ a lot of interest in that thinking. Some of us are math nuts;some are not.I don't pass judgment on those who are not. I suppose I could add as an addendum that the same could be said of our gun laws issue.

quote:

In my little world I have to ask - who cares ?

When I didn't know ^ meant to the "power" I knew I was over my head.

quote:

Originally posted by ramrod340:

quote:

In my little world I have to ask - who cares ?

When I didn't know ^ meant to the "power" I knew I was over my head.

The ^ is used in when making things in Access and Excel etc. and also at times in general writing. However, programs like MS Access or Excel are not needed for this.

5² will be what you are used to instead of 5^2

You might at times see something like 6*7 which is 6 X 7 but the * is used in stuff like Access etc. instead of X. In those programs if 6 X 7 or 6X7 was used the program would read it as written, that is, not read the X for multiply.

Fully understand.. Heck I used both a Post and Pickett slide rule in getting my engineering degrees. So I could adjust.

Sometime ago I posted this same problem on Australia's biggest Guns/Hunting site and response was small although bigger than AR. I think that is because on the Australian site (which is as active AR, probably more so) I could put it Off Topic and that is one of their most active forums whereas Miscellaneous not quite so on AE.

The biggest response was a data base forum I am on and I suppose that is not surprising. No one got it but a couple came close. One of the answers that is often missed needs arithmetic at maybe age 9 or similar. Some very good lateral thinkers get that answer but hit a wall with a few of the others as they have forgotten high school arithmetic as they no longer use it. Simple arithmetic is all that is needed, no algebra, calculus, trigonometry or witchcraft.

TomP said he has the answers but have not heard back from so at this stage things still stand unchanged, only one person I have seen who could do all 12 answers.

Mike, here is one of my Dad's favorite riddles.

Lots of folks miss it it a few get it right off so I am putting it on here for you.

You have two ducks in front of a duck and two ducks behind a duck and a duck in the middle, how many ducks have you got?

5

When it comes to lateral thinking I am sure there must be at least one person in the world who is worse than me. The dentist who solved the "three 2s" has the greatest lateral thinking I have even see. We have know each other since we were about age 7.

Lateral thinkers are great at getting an invention basically off the ground. They are also great at getting an initial hand on solving a problem. On the other hand the very poor latera; thinker who has similar knowledge, intellect etc. is much better at developing the invention or takin the solution to a problem though to the most refined end.

One has very broad but shallow thinking and the other has very narrow but deep thinking.

Back in 1971 I was in a course with about 20 people. We were asked how many things you could use a paper clip for. The non latera; thinkers like myself wrote down all the things I could think of you could use a paper clip for. The lateral thinkers wrote down what you could use a paper clip for BUT also what you could use the piece of wire for when you straightened out the paper clip.

Each of read out our answers I and I still remember like it was yesterday when I heard the first bloke with the paper clip tuned into a straightened out bit of wire. My reaction was "why the fuck didn't I think of that"

The group was then asked to do the test again. This time the very poor lateral thinkers like myself were top of the group instead of being last. The lateral thinkers were now last. Second time around we had a lot more answer for what a paper clip could be used for but it was the lateral thinkers in session 1 that were responsible.

I'm sure it's not 5;that would be too easy. Reminds me of the poem/riddle of "As I was going to St. Ives."Not sure of the answer yet Randle;lets give it a few days then I would like to know.

quote:

Originally posted by Mike McGuire:

quote:

Originally posted by TomP:

Got it, but I'm not going to spoil the ending...

And you always have three 2s, not more not less on one side?

So 2/2 = 1 would not qualify.

If you have got it then you are the second person I have seen do it since about 1970.

When I first saw it I could not do it and the person who gave it to me did not have the answers.

Oops. Only twos but five of them.

((2^2)^2) - (2^2) = 12

or four

(22+2)/2 = 12

Back to the drawing board.

quote:

Originally posted by TomP:


Oops. Only twos but five of them.

((2^2)^2) - (2^2) = 12

or four

(22+2)/2 = 12

Back to the drawing board.

Don't worry, I have posted the problems in all sorts of ways and no matter which was the message is not clear \

I will give you a clue on getting 12.

To get 12 is almost identical to the way you get 8

quote:

Originally posted by NormanConquest:
I'm sure it's not 5;that would be too easy. Reminds me of the poem/riddle of "As I was going to St. Ives."Not sure of the answer yet Randle;lets give it a few days then I would like to know.

5 does require being familiar with arithmetic. However, I am sure 100% of people would instantly understand how the calculation is done. Lateral thinking.

Another clue. Getting 5 is related to getting 8 and 12. Another clue, although it does not go to 20, getting 20 would also relate to getting 12, 8 and 5.

Again, one of the answers is so simple from an arithmetic point of view I reckon someone who never learned to read or write would understand the answer. If he worked as a shop keeper or was selling something etc. he would not only understand the answer but probably does the same type of calculation every hour of every day.

quote:

Originally posted by Mike McGuire:

quote:

Originally posted by TomP:

Oops. Only twos but five of them.

((2^2)^2) - (2^2) = 12

or four

(22+2)/2 = 12

Back to the drawing board.

Don't worry, I have posted the problems in all sorts of ways and no matter which was the message is not clear \

I will give you a clue on getting 12.

To get 12 is almost identical to the way you get 8

Fair?
((2+2)!)/2 = 12

Unfair?
(2/.2) + 2 = 12

quote:

Originally posted by TomP:

Unfair?

(2/.2) + 2 = 12

Correct

From an arithmetic point of view 7 and 10 are the toughest but still high school arithmetic, no algebra, calculus but lots of lateral thinking.

One other tip. Any mathematical symbol used will be understood by anyone on the forum.

quote:

I'm sure it's not 5;that would be too easy. Reminds me of the poem/riddle of "As I was going to St. Ives."Not sure of the answer yet Randle;lets give it a few days then I would like to know.

Okay, I will give the answer New Years Day, unless someone gets it sooner.

Keep in mind this came from a man that was born in 1897 and did not finish the Third grade and he was 54 when I was born. He always got a kick out of messing with people with it.

! Isn’t simple mathematics

quote:

Originally posted by Mike McGuire:
One other tip. Any mathematical symbol used will be understood by anyone on the forum.

Does 2^2 count for one two, or two twos?

22/2 = 11?

quote:

Originally posted by ramrod340:
! Isn’t simple mathematics

I know and note the correct answer I posted for TomP and the post I made about symbols

quote:

Originally posted by TomP:

quote:

Originally posted by Mike McGuire:
One other tip. Any mathematical symbol used will be understood by anyone on the forum.

Does 2^2 count for one two, or two twos?

22/2 = 11?

22/2 = 11 Correct

2^2 counts as two 2s because you are actually writing 2²

quote:

Originally posted by Mike McGuire:

quote:

Originally posted by TomP:

quote:

Originally posted by Mike McGuire:
One other tip. Any mathematical symbol used will be understood by anyone on the forum.

Does 2^2 count for one two, or two twos?

22/2 = 11?

22/2 = 11 Correct

2^2 counts as two 2s because you are actually writing 2²

So 7 and 9 have me puzzled. No matter, there are two days left.

quote:

Originally posted by TomP:

So 7 and 9 have me puzzled. No matter, there are two days left.

List what you have.

If don't have 7 I would be surprised if you have 10

If don't have them a clue for 8 and 9. You already have the basis for them.

quote:

Originally posted by Mike McGuire:

quote:

Originally posted by TomP:

So 7 and 9 have me puzzled. No matter, there are two days left.

List what you have.

If don't have 7 I would be surprised if you have 10

If don't have them a clue for 8 and 9. You already have the basis for them.

2 - (2/2) = 1
2^(2-2) = 1

2+2-2 = 2
2^(2/2) = 2

2+(2/2)=3

SQRT(2) x SQRT(2) + 2 = 4
SQRT(2) x SQRT(2) x 2 = 4

(2/2)/(.2) = 5
2/(2*.2) = 5

2+2+2 = 6
((2/2)+2)! = 6

7?

2x2x2=8
2*(2^2) = 8
(2/.2)-2 = 8

9?

(SQRT(2) x SQRT(2))/(.2) = 10

22/2 = 11

((2+2)!)/2 = 12
(2/.2) + 2 = 12

(2+2)!)/2 = 12 Only symbols that anyone would know what they are.

(2/.2) + 2 = 12 Correct

Nice job TomP! You got more than I did!
I am puzzled by your use of the factorial (!, exclamation point) though.
Peter.