Think of any positive number. Multiply it by itself and subtract negative 3 from it. Then add the original number four times. Divide your resultant number by one more than the original number. Lastly, take the resultant number and subtract off the original number. I know what number you have. What must it be?
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I don't seem to get the solution when I picked '2'
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The only explanation can be that you subtracted 3 instead of subtracting -3 which would ultimately give you +3.
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Why did it not just say add 3 to begin with?
2×2=4, 4+3=7, 7+(2×4)=15, 15/(2+1)=5, 5-2= 3
yeah for me too
2 doesn't work, aswell as one
That happened to me the first time as well. But you're subtracting a negative 3, meaning you're adding 3 (- + - = +). Therefore: (2x2=4) (4+2+2+2+2=12) (12-(-3)=15) (15/3=5) (5-2=3) 3 is your answer.
If your original number is 2 the result is one which makes it all wrong
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The same thing goes to 1
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1 also works. I think you made a mistake in your math somewhere
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@Mary-Mae Humphrey – Please explain?
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@Avinash Kamath – You must have misunderstood and miscalculated the part of "Subtract negative 3".
are you sure??
I got 1 when I used 2
The actual Procedure =>
2 × 2 = 4,
4 - (-3) = 4 + 3 = 7
7 + (2 × 4) = 15
15 / (2 + 1) = 5
5 - 2 = 3.
Perhaps you did like this =>
2 × 2 = 4
4 - 3 = 1
1 + (2 × 4)= 9
9 / (2 + 1) = 3
3 - 2 =1.
I would just say ... look twice before you leap.
did you add (-3)
No, 2 works just the same
After all the processes the number remaining is 3 => for every value of x the answer we get is 3. Unbounded solution i.e, all positive integers are acceptable.
It is brilliant, though confusing. You don't need to choose a positive number though, you just need to choose any number that is not -1
When subtracting it should have been x^2 - 3, not + 3.
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subtracting negative three means adding 3
The important thing to notice is the (-3) we are really subtracting from any number n squared (the first clue). So the basic equation to set us on the right path is n^2 - (-3) = n^2 + 3. Then we add 4x the original number n to the equation which gives us n^2 + 3 + 4n. Lastly, we take the latest expression and divide it completely by one more than the original number n giving us (n^2 + 3 + 4n) / (n + 1). For algebra connoisseurs, the top expression can be factored as it is a factorable trinomial. In other words, (n + 1) (n + 3) = n^2 + 3n + 1n + 3 OR similarly, by adding the two middle terms 3n and 1n --》(n + 1) (n + 3) = n^2 + 4n + 3.
Notice how factoring the top makes it easier on on the mind or "eyes" to algebraically solve this as (n + 1) (n + 3) / (n + 1) from the above expression, giving us a same term (quantity) in the numerator as well as in the denominator, (n + 1) that therefore cancel out. This leaves the rest as n + 3, which is still unresolved because the last clue given was to lastly subtract the original number n by itself which written out concludes n - n + 3 which is just 3.
And this is why mixing numerical terms with written terms is a poor idea--maybe logically valid, but definitely not coherent or clear.
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It is, provided you look carefully, that is.
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I beg to differ. The problem is laid out specifically to exploit the distinction between the written "negative" and the numeric "3", anticipating the omitted nuance when translating them into a unitary referencing system.
In other words, I was merely pointing out the core of the problem is an opportunistic exploitation of the inability for human brains to quickly switch between two different (and usually separate) notational styles--a lesson, as it were, against mixing numbers and words (or any other two distinct lexicographic systems) without extreme care and caution.
[I point that out primarily because I do this quite often, actually...though, I have to admit, it's also because this problem doesn't rely on reason or logic, but merely a common cognitive fallacy. Basically, I find people using parlor tricks to prove how "clever" they are to be a titch annoying sometimes...]
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@Joshua Nesseth
–
Subtract ==> [ – ]
Negative ==> [ - ]
3 / Three ==> [ 3 ]
Subtract negative 3 ==> – (-3) = + 3 ✓
First we take the no. as x. Afterwards,as we follow the given steps, we get a quadratic equation which is :- x^2+4x+3, which on solving, we get 3 as an answer..
As in a previous puzzle, since the result does not depend on what number was chosen, choose 0 to simplify the arithmetic.
x^2 - (- 3) x^2 + 4x + 3 x^2 + 4x + 3 / x +1 x + 3 x + 3 - x
3
1) Think of any positive number ==> x
2) Multiply it by itself ==> x × x = x²
3) Subtract negative 3 from it ==> x² – (-3) = x² + 3
4) Add the original number four times ==> x² + 3 + (x × 4) = x² + 4x + 3
5) Divide your resultant number by one more than the original number ==> (x² + 4x + 3) / (x + 1) = x + 3
6) Lastly, take the resultant number and subtract off the original number ==> (x + 3) – x = 3
Universal answer = 3
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Let x be the number. Now, by multiplying it by itself we obtain x 2 , now by subtracting − 3 we have x 2 + 3 . Adding four times the number: x 2 + 4 x + 3 , but it can also be ( x + 1 ) ( x + 3 ) . Finally, dividing it by one more than the original number: x + 1 ( x + 1 ) ( x + 3 ) , or x + 3 since x is positive, and subtracting the original number: 3 .