Really tough. I started with 8** and 7** and found out the difference as 49. Since 49 was already present as an answer choice, I marked it.

to get the minimum difference, we find minim difference in hundred digits, which are
1 and 2
2 and 3
6 and 7
7 and 8

now we need to find the greatest 2-digit number and smallest 2-digit number to add the greatest to the number with smaller hundred digit and add the smallest to the number with greater hundred digit

for the first couple, we have 3,6,7,8, and we can find 87 and 36
for the second couple, we have 1,6,7,8 and we can find 87 and 16
for the third couple, we have 1,2,3,8 and we can find 83 and 12
for the forth couple, we have , 1,2,3,6 and we can find: 63 and 12

now we do
smaller 2 digit number-greater 2 digit number, adding 1 to be hundred digit of the smaller
1 36-87=59
1 16-87=29
1 12-83=29
1 12-83=29

answer is 29

N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?

Let N be n1n2n3 and let M be m1m2m3

min (|100(n1-m1) + 10(n2-m2) + (n3-m3)|) = ?

Let N be 287
Let M be 316
316 - 287 = 29

IMO A
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