Brain Teasers
2 and 2 = 5
Two 2s can be combined in many ways to express different numbers. Here are some!
2-2=0
2/2 = 1
.2 + 2 = 2.2
(2^2)! = 24 (4! means 4x3x2x1) (2^2 is 2 to the power of 2)
**CHALLENGE!**
Can you write an expression that has the value of exactly 5, using:
* two, and only two, 2s, and
* any mathematical symbols or operations?
You may not use any other numbers. The symbols used would be known by most high school maths students.
The hint below lists the symbols that are used in this solution. Even with that information, it is a worthy challenge!
Of course, other solutions may be possible! Solvers should write these in the Comments section.
2-2=0
2/2 = 1
.2 + 2 = 2.2
(2^2)! = 24 (4! means 4x3x2x1) (2^2 is 2 to the power of 2)
**CHALLENGE!**
Can you write an expression that has the value of exactly 5, using:
* two, and only two, 2s, and
* any mathematical symbols or operations?
You may not use any other numbers. The symbols used would be known by most high school maths students.
The hint below lists the symbols that are used in this solution. Even with that information, it is a worthy challenge!
Of course, other solutions may be possible! Solvers should write these in the Comments section.
Hint
These operations or symbols are used, in some order:* exponent (index or power)
* a minus (-) sign
* brackets
* square root
* a decimal point
Answer
The square root of point 2 to the power of minus 2.sqrt ( (.2)^(-2) )
.2^(-2) is the same as 1/0.04, i.e. 25
[Point 2 is usually written as 0.2, but .2 is also correct.]
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Comments
Excellent puzzle! It took me a while, but I was finally able to solve it. Thanks for your contribution, a very high-quality brain teaser!
Very tricky. I didn't get it until I used the clue. Deserves a "Fun" grade even though I didn't really get a huge amount of 'fun' out of the challenge!!
Thanks TFF and Gran Yes, I enjoy the maths challenges and like writing them for my students. Glad you enjoyed this one too.
2! + ∑2
Just for fun, this uses only ONE 2 (Roman numeral "V" = 5):
__
√V ²
__
√V ²
*cnmne* ??? Not sure about your use of sigma there. According to my understanding of the symbol, that's incomplete. "Sum 2" has no meaning that I know of. Enlighten me?
Wow! This was rough!
And beautiful. A true math teaser.
I came up with an alternate fairly quickly, but then looked at the hint and really had to work to get the intended answer.
My alternate:
[sec(arctan(2))]^2
Picture a right triangle with sides 1,2,sqrt(5)
And beautiful. A true math teaser.
I came up with an alternate fairly quickly, but then looked at the hint and really had to work to get the intended answer.
My alternate:
[sec(arctan(2))]^2
Picture a right triangle with sides 1,2,sqrt(5)
2x2=4+2/2=5
Good one, Snowdog - I can challenge my senior class to revise trig with this; hadn't thought of it.
Freddo, your solution doesn't work - the rule requires two 2s and you use two pairs of 2s.
Any other solutions??
Freddo, your solution doesn't work - the rule requires two 2s and you use two pairs of 2s.
Any other solutions??
Nice one, thanks!
My solution: ceil(sqrt(log((2+2)!!)))
Ceil is the ceiling operation (round up to the next integer; ceil(2.1) is 3, ceil(3) is also 3). (2+2)!! is 24!, the log of which is 23.7927...
The ceiling operation can also be indicated by partial brackets with tops but no bottoms.
Ceil is the ceiling operation (round up to the next integer; ceil(2.1) is 3, ceil(3) is also 3). (2+2)!! is 24!, the log of which is 23.7927...
The ceiling operation can also be indicated by partial brackets with tops but no bottoms.
I veer away from anything that has to do with math. It is not my kind of teaser, but thanks anyway for posting. Tomorrow is another day!
Sorta agree with Babe.
Although I did well in maths in school I find some of these math teasers quite daunting.
If you want a more entertaining read go take a look at my comment on Jakes "Knowledge" (#5184 teaser of a few days ago.
And ... to coolnana; try to apply a bit of sense (and patience) to the 'tirades' on comments.
Comments are our best indicators of visitation. And visitation (across the boards) to Braingle is rapidly declining. Check it out. Don't just take our word for it.
THAT is what we care about.
Thanks for reading.
Jaye (and ... we are STILL ... ) langhing
Although I did well in maths in school I find some of these math teasers quite daunting.
If you want a more entertaining read go take a look at my comment on Jakes "Knowledge" (#5184 teaser of a few days ago.
And ... to coolnana; try to apply a bit of sense (and patience) to the 'tirades' on comments.
Comments are our best indicators of visitation. And visitation (across the boards) to Braingle is rapidly declining. Check it out. Don't just take our word for it.
THAT is what we care about.
Thanks for reading.
Jaye (and ... we are STILL ... ) langhing
Am I missing something? My solution was [(2x2x2) + 2]/2
which would also equal 5. Wouldn't it?
which would also equal 5. Wouldn't it?
Ah, I'm happy to see this beauty as a teaser of the day. I had to check the hint again in order to get the requested answer. I really like this one. It's going into my favorites.
I'm glad this is still being enjoyed, and that a few nerds are finding complicated alternative solutions. I would remind you, however, that the symbols used are supposed to be those commonly known to most high school students. Also, ONLY two 2s are to be used.
Cheers
Cheers
[(2²)! - 2²]/2² = (24 - 4)/4 = 20/4 = 10/2 = 5
One Two: e^(ln(-.2)).
Correction: One Two: e^(-ln(.2)).
I love math but this was a little too advanced for me. I would have gotten this when I was younger but I have been away from math too long and do not remember a lot of stuff.
2 divided by 2 + 2 + 2
Why you all put complicated sentences.
Why you all put complicated sentences.
am i understanding this incorrectly because i feel like there is a lot of much simpler answers
0.2 raised to i (imaginary number) raised to 2
Sorry... adding a little clarity to my answer so that the order of ops is clear... 0.2^(i^2).
assumption: since the factoral symbol is legal in this puzzle which has mathematical implications that involve other numbers besides 2 (2! involves 1 and 2), that the i is also legal since it involves the 1 just like the factoral does.
Now my braingle hurts
assumption: since the factoral symbol is legal in this puzzle which has mathematical implications that involve other numbers besides 2 (2! involves 1 and 2), that the i is also legal since it involves the 1 just like the factoral does.
Now my braingle hurts
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