Any great minds or big thinkers - can you solve this arithmatic level yet sophisticated maths problem !!?

Question

If you multiply me by 2, subtract 1, and read the reverse the result you'll find me. Which numbers can I be?

no its not 1 - one is not the answer - there are more then one answer but definitely not one - the answer starts with a two digit number

Sciencenut - that was not what I meant, though what you said of it being odd numerical is right. Lets say - My question is pretty simple it means what it says.

try converting it in to an algebraic equation and solve it from there - two digits there is only one , three digits there is one , four digits there is one and so on

z32486 - you are wrong , I am surprised since this is a simple arithmetic problem which I was creating a simple VB program and many find it difficult

holdm - can you rephrase your answer

bravo NancyB - you are absolutely correct - Yahoo Answer wouldn't let me yet to choose your answer as the best answer since I have to wait 4 hours more to do that

Answer 1

For a 1-digit number, A,
2A - 1 = A
Therefore, A = 1.

For a 2-digit number, AB (= 10A + B),
2(10A + B) - 1 = 10B + A
So, 19A - 8B = 1
Therefore A = 3, B = 7, so, AB = 37.

For a 3-digit number, ABC (= 100A + 10B + C)
2(100A + 10B + C) - 1 = 100C + 10B + A
ABC = 397

A pattern continues (I don't know for how long) -
For a 4-digit number, ABCD = 3997.
For a 5-digit number, ABCDE = 39997.
For a 6-digit number, ABCDEF = 399997.

I think it goes on forever, as 39.....97 may be
represented as 4*10^n - 3 and 79.....93 may be
represented as 8*10^n - 7.
The equation : 2 * (4*10^n - 3) - 1 = 8*10^n - 7
is true for all n, as it is an identity.

Method to calculate for the 2-digit number, AB :
We have 19A - 8B = 1
Therefore, B = (19A - 1) / 8
Expand : B = 2A + (3A - 1) / 8
Let (3A - 1) / 8 = J, as it must be an integer.
Therefore, A = (8J + 1) / 3
Expand : A = 2J + (2J + 1) / 3
Let (2J + 1) / 3 = K, as it must be an integer.
Therefore, J = (3K - 1) / 2
Expand : J = K + (K - 1) / 2
Let (K - 1) / 2 = M, as it must be an integer.
Therefore, K = 2M + 1
Substituting back :
J = 3M + 1
A = 8M + 3
B = 19M + 7
A and B are each single digits, so M must be zero.
Therefore, A = 3 and B = 7.

Answer 2

1

Answer 3

They are all numbers which start with 3, end with 7 and have 9's in the middle.

37 -> 73
397 -> 793
3997->7993
39997 ->79993
399997 ->799993
etc

If the number is AxyzB , it's reverse is BxyzA - so A and B must fit digits such that 2B -1 = last digit of A and 2A or 2(A+0.5)=first digit of B

3 and 7 are the only numbers that fit this.

Looking for a 3 digit number

3N7=7N3

So 2N+1 = N-10
(2x7 =14 so carry the 1 - and we know that 2N must be enough to carry the 1 to make the 7 in the hundreds column)
=> N=9

In the same way when we are looking for a 4 digit number
3xy7 x2-1 = 7yx3

gives
2x-1=y+10
2y-1=x+10
Which solve to x=y=9

And so on...

Answer 4

I believe the answer is x = 1 and only 1.
I'm not sure how to set a problem like this up mathematically, the problem is how to you obtain the reverse of a number mathematically.
2x-1 = reverse formula
you could solve for x then if such a formula existed

OH i see holdm's answer, good answer holdm
hes right

Answer 5

assume a 2-digit number 10x+y
20x + 2y - 1 = 10y + x
19x -8y = 1
x = 3, y = 7 37

Answer 6

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Answer 7

I think another way of expressing your question is, "which odd numerals are bilaterally symetrical?" The number one is the only odd integer. However, 0.5, 1, 4.5, 6, etc., etc. might be an infinite solution set.