Utkrisht123 3 Report post Posted March 21, 2013 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? Share this post Link to post Share on other sites

0 TimeSpaceLightForce 11 Report post Posted March 21, 2013 (10a+b) (10c+d) = (10b+a) (10d+c) 63 X 48 = 36 X 84 Share this post Link to post Share on other sites

0 TimeSpaceLightForce 11 Report post Posted March 21, 2013 (10a+b) (10c+d) = (10b+a) (10d+c) 24 X 63 = 42 X 36 Share this post Link to post Share on other sites

0 dark_magician_92 4 Report post Posted March 21, 2013 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 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.... Share this post Link to post Share on other sites

0 Debasis 0 Report post Posted March 21, 2013 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.. Share this post Link to post Share on other sites

0 TimeSpaceLightForce 11 Report post Posted March 21, 2013 (edited) ( 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 March 21, 2013 by TimeSpaceLightForce Share this post Link to post Share on other sites

0 nakulendu 2 Report post Posted March 22, 2013 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 Share this post Link to post Share on other sites

0 nakulendu 2 Report post Posted March 22, 2013 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 pure 2 digit pairs - 12 and tohose which have a 1 digit number as well as above - 4 Share this post Link to post Share on other sites

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?

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