MathDB

6

Part of 2007 Postal Coaching

Problems(2)

distance between two 5-digit numbers

Source: Indian Postal Coaching 2007 set 3 p6

5/25/2020
De fine the distance between two 55-digit numbers a1a2a3a4a5‾\overline{a_1a_2a_3a_4a_5} and b1b2b3b4b5‾\overline{b_1b_2b_3b_4b_5} to be the largest integer jj such that aj≠bja_j \ne b_j . (Example: the distance between 1652316523 and 1645216452 is 55.) Suppose all 55-digit numbers are written in a line in some order. What is the minimal possible sum of the distances of adjacent numbers in that written order?
number theorySum
no 2 of them have the property that one divides other, in 7-digit numbers

Source: Indian Postal Coaching 2007 set 6 p6

5/25/2020
Consider all the 77-digit numbers formed by the digits 1,2,3,...,71,2 , 3,...,7 each digit being used exactly once in all the 7!7! numbers. Prove that no two of them have the property that one divides the other.
Digitsnumber theorydividesdivisible