Brain Teasers
Arithmetical Bedlam Conundrum
You have the following equations:
a + c = a
b - c = c
c / b = c
a * a = b
You also know that a, b, c have the values 0, 1 and 2, but not necessarily in that order.
But to make matters more complicated the symbols + - * / have been mixed up: all you know is that each represents a different arithmetical operation (addition, subtraction, multiplication or division).
Can you work out the values of a, b and c, and what each of the symbols actually mean?
a + c = a
b - c = c
c / b = c
a * a = b
You also know that a, b, c have the values 0, 1 and 2, but not necessarily in that order.
But to make matters more complicated the symbols + - * / have been mixed up: all you know is that each represents a different arithmetical operation (addition, subtraction, multiplication or division).
Can you work out the values of a, b and c, and what each of the symbols actually mean?
Hint
The only thing you should assume about the arithmetical symbols is that no two represent the same operation.Answer
a = 1b = 2
c = 0
+ = -
- = *
* = +
/ = /
(Yes, the division symbol escaped the bedlam!)
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Comments
Great teaser, it was fun trying to figure out the symbols!
However, there is a second answer to your teaser.
a = 2
b = 0
c = 1
+ = *
- = +
/ = /
* = -
2 * 1 = 2
0 + 1 = 1
1 / 0 = 1
2 – 2 = 0
However, there is a second answer to your teaser.
a = 2
b = 0
c = 1
+ = *
- = +
/ = /
* = -
2 * 1 = 2
0 + 1 = 1
1 / 0 = 1
2 – 2 = 0
I submitted that correction.
1/0 = infinity
Hmm, I suppose you're right, Mikey. I was thinking of it more in a pie sense. If I have one pie and I cut it 0 times, I'm still left with a whole pie (though I'd love an infinity of pies!). Seems logical...
Rather simple, with a little bit of trial and error effort!
1/0 is not infinity. It is undefined. lim (x-->0) of 1/x approaches infinity.
I agree and backup Udoboy. Any number divided by zero equals undefined. Try it on a calculator or look it up in a good math book.
I'll exept that answer, but my calculator has never given infinity for any answer. Can anything ever equal infinity, or will it only approach infinity?
nice one
mikey infinity itself is undefined... so I don't know if anything can really equal infinity... I got the answer that was provided in the teaser after a little logic... what I didn't like about the teaser is that I didn't get the answer until I looked at the hint because the way the teaser was asked would make one assume that none of the operators actually represented its actual mode of action.
Interesting, wiz. It was fun and easy, until I realized I got a valid, yet alternate and unlisted answer. Then I felt gypped.
Also didn't like how one operation = itself. The teaser wording inferred (though not clearly stated) that the operations would each = something different.
Still a fun idea though.
Also didn't like how one operation = itself. The teaser wording inferred (though not clearly stated) that the operations would each = something different.
Still a fun idea though.
Fun and easy. Well done!
Yeah, that was fun, even though I had thought that the operations were supposed to /certainly/ not be what they looked like. I ended up with what I thought was a valid answer, but then the Hint set me straight (I had two +'s).
This was a well put together teaser! (And yay, by rating this one, I earned enough rank to mark comments as offensive! Look out world!)
This was a well put together teaser! (And yay, by rating this one, I earned enough rank to mark comments as offensive! Look out world!)
Oh, by the way, I just had a giggle about the "division by zero" thing...
If I have a pie, and cut it into ZERO pieces .... hmm, now where'd that darn pie go?!
Maybe the pie got blasted into so many pieces that the pieces themselves are too small to be seen by the naked eye. Why, there'd have to be almost an infinite number of pieces cut for that to happen!
If I have a pie, and cut it into ZERO pieces .... hmm, now where'd that darn pie go?!
Maybe the pie got blasted into so many pieces that the pieces themselves are too small to be seen by the naked eye. Why, there'd have to be almost an infinite number of pieces cut for that to happen!
Sigh... I *hate* it when people don't understand the concept of division by zero.
The limit as x approaches 0 of 1/x is indeed infinity, but 1/0 is undefined. Think of it this way... if 1/0 is equal to infinity, then is 0 * infinity = 1? Certainly not.
The limit as x approaches 0 of 1/x is indeed infinity, but 1/0 is undefined. Think of it this way... if 1/0 is equal to infinity, then is 0 * infinity = 1? Certainly not.
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