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Find the number of positive integral solutions

Source: MTRP 2019 Class 11-Multiple Choice Question: Problem 3 :-

April 9, 2020
number theory

Problem Statement

Find the number of positive integral solutions to the equation ∑i=1201910ai=∑i=1201910bi\sum \limits_{i=1}^{2019} 10^{a_i}=\sum \limits_{i=1}^{2019} 10^{b_i}, such that a1<a2<⋯<a2019a_1<a_2<\cdots <a_{2019} , b1<b2<⋯<b2019b_1<b_2<\cdots <b_{2019} and a2019<b2019a_{2019} < b_{2019}
[*] 1 [*] 2 [*] 2019 [*] None of the above
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