[Guest]

N is a four digit number that does not end in a zero. R(N) is the four-digit integer

obtained by reversing the digits of N. For example R(3275) = 5723.

There is only one integer for which R(N) = 4N + 3. What is it?

[Guest]

1997

Way to get it:

We have N = N1 N2 N3 N4

Now, we know N1 is odd, because 4N is even and if you add 3 you get an odd number.

Also, we know that N1 has to be smaller than 3. Otherwise, multiplication by 4 leads to a number with 5 digits.

So N1 = 1.

Next step.

Figure out N4. It has to be at least 4. Because N1=1.

R(N)=4N +3 =>

4N = N4 N3 N2 N1 - 3

4N = N4 N3 N2 1 - 3

4(N1 N2 N3 N4) = N4 N3 (N2-1) 8

Now you can see N4 has to be 7.

Next step.

If N4 is 7 then N2 has to be 8 or 9 to obtain this high a number for R(N), which is now in the 7000's.

By trial and error it easy to figure out that the correct number is 1997.

Edited October 21, 2011 by Henoch

[robo]

1997

[dark_magician_92]

1997

R-N=3(N+1)

IF N=1000A+100B+10C+D

THEN ON PUTTING VALUES

1=332D+20C-130B-1333A

R<=9999, SO N<2500, SO A=1 OR 2,

R=4K+3, SO ITS ODD HENCE A IS ODD SO A=1, HENCE D CAN BE 5 OR 7,

SO 1334-332D=10*(2C-13B), HENCE LHS SHUD BE A MULTIPLE

OF 10 SO D CAN BE 2 OR 7 ONLY, SO IT HAS BE 7, PUT D=7 TO GET B AND C

1997