7 replies to this topic

[Utkrisht123]

Look at this pair

   42                         24                                                 ( digits of 42 are interchanged i.e =24)

x 48                       x 84                                                 (digits of 48 are interchanged i.e = 84)

--------                   ----------

 2016                      2016

 

When the digit of multiplicand and multiplier are interchanged then also the result is same.

How many such pair can you find?

[TimeSpaceLightForce]

Spoiler for starter

(10a+b) (10c+d) = (10b+a) (10d+c)

             63 X 48  = 36 X 84 

     

[TimeSpaceLightForce]

Spoiler for another

(10a+b) (10c+d) = (10b+a) (10d+c)

               24 X 63  = 42 X 36

         

[dark_magician_92]

Look at this pair

   42                         24                                                 ( digits of 42 are interchanged i.e =24)

x 48                       x 84                                                 (digits of 48 are interchanged i.e = 84)

--------                   ----------

 2016                      2016

 

When the digit of multiplicand and multiplier are interchanged then also the result is same.

How many such pair can you find?

If you are asking for 2 digit numbers, then

Spoiler for

lets say the numbers are AB and CD, then this property is true if A*C=B*D. eg. 14*82, 24*63 and so on....

[Debasis]

Spoiler for got the solution

let the two numbers be=10a+b and 10x+y so acc. to given condition , (10a+b)* (10x+y)=(10b+a)*(10y+x)

solving we get ax=by in such cases ....so there can be infinetely many possible combinations in which AB*XY=BA*YX

the only req. is A*X=B*Y..

[TimeSpaceLightForce]

Spoiler for

( 10Na+a )(10b+Nb)=(10a+Na)(10Nb+b)

N(2,3,4)

12:  42 84 63         6 pairs

13:  62 93             3 pairs

14:  28                  1 pair

Edited by TimeSpaceLightForce, 21 March 2013 - 04:34 PM.

[nakulendu]

Spoiler for I got

10 pairs in all.

6 of the pairs are truly 2 digit number pairs:
1. (12, 42 ) (21, 24)
2. (13, 62 ) (31, 26)
3. (14, 82 ) (41, 28)
4. (23, 64) (32, 46)
5. (24, 84) (42, 48) ... already listed
6. (34, 86) (43, 68)

4 additional the pairs can be had where there is a 1 digit number in each pair e.g. you take 1 as 01 and the reversing digits you get 10
). These are
a. (1, 20) (10, 2)
b. (2,40) (20,4)
c. (3,60) (30,6)
d. (4,80) (40,8)

I guess this is it.

Didn't get into 3 digit numbers because rules of switching digits as shown in example gets cloudy

[nakulendu]

Spoiler for I got

10 pairs in all.

6 of the pairs are truly 2 digit number pairs:
1. (12, 42 ) (21, 24)
2. (13, 62 ) (31, 26)
3. (14, 82 ) (41, 28)
4. (23, 64) (32, 46)
5. (24, 84) (42, 48) ... already listed
6. (34, 86) (43, 68)

4 additional the pairs can be had where there is a 1 digit number in each pair e.g. you take 1 as 01 and the reversing digits you get 10
). These are
a. (1, 20) (10, 2)
b. (2,40) (20,4)
c. (3,60) (30,6)
d. (4,80) (40,8)

I guess this is it.

Didn't get into 3 digit numbers because rules of switching digits as shown in example gets cloudy

Spoiler for Sorry - a few more

pure 2 digit pairs - 12
and tohose which have a 1 digit number as well as above - 4