Need Of Difference

[Raiyan Jamil]

Two two digit numbers are made by using the digits 1 , 3 , 5 , 6 , 8 only once so that their difference is minimum . What is the lowest difference and what are those numbers ?

[Nayeemul Islam Swad]

Are $12$ and $21$ valid two numbers? I mean each digit can occur at most once. But is it in the sense of just one number?

[Raiyan Jamil]

Raiyan saying ,
No , 12 and 21 can' t be taken . 1) as 2 is not in the list . 2) the two two digit numbers are to be made with 4 numbers from the given 5 numbers .

[asif e elahi]

$63-58=5$

[Nayeemul Islam Swad]

Let the numbers be $10a+b$ and $10c+d,$ $10a+b>10c+d.$ Then their difference is $10(a-c)-(d-b).$ Now, the minimum possible value of $a-c$ is $1(a=6$ and $c=5)$ and the maximum possible value of $d-b is$ $7(d=8$ and $b=1).$ So the required two numbers are $61$ and $58$ and their difference is $3.$

[Raiyan Jamil]

#asif your ans is not correct instead of using 63 , use 61 , then you will find 3 instead of 5 .
# look nayeemul's ans .

[asif e elahi]

ooops......$63-58=5$ is the 2nd lowest difference.