Let $\overline{ABCD}$ be a $4$-digit number. What is the smallest possible positive value of $\overline{ABCD}- \overline{DCBA}$?
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Tags: number theory, Digits
14.09.2021 22:21
Do different letters represent different numbers?
14.09.2021 22:23
not necessarily
14.09.2021 22:27
the result has 2 digits, it asks for smallest positive
14.09.2021 22:28
no 1119 - 9111 = -7 992 it's smaller
14.09.2021 22:31
9999 - 9999 = 0 the smallest possible number no ? Is it positive or strictly positive ?
14.09.2021 22:36
positive means greater than zero
14.09.2021 22:52
90. Simply expand, and you get that it's equal to 999(A-D) + 90(B-C), and since B-C < 10, and we can't have A-D > 0, thus A=D and B-C = 1.
14.09.2021 23:01
14.09.2021 23:08
fuzimiao2013 wrote: 90. Simply expand, and you get that it's equal to 999(A-D) + 90(B-C), and since B-C < 10, we can't have A-D > 0, thus A=D and B-C = 1. Sorry, could you explain why A-D must be greater than 0 if B-C<10.
15.09.2021 05:10
yuh
15.09.2021 18:05
Yeah, I figured it out using the "common sense" approach that we are looking for the smallest positive integer but I still don't understand @fuzimiao2013's solution