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I need a hint. Please give me a hint.
Let’s assume 1000a+100b+10c + d is a memorable year where a, b, c, d ∈ Z2 ≤ a ≤ 9; 0 ≤ b, c, d ≤ 9. [That means they are valid digits in base 10.]
They must satisfy the equation,
10a+b+10c+d10b+c
10a+9c+d=9b
To get the minimum such year after 2018, let’s guess a = 2.
So, 20+ d = 9(b - c).
Since 9 20+ d and 20 ≤ 20+ d ≤ 29,
We must have, 20+ d27d=7
From here, we conclude, bc 3. To minimize the value of b, let’s use the solution b = 3, c = 0. From here, we conclude that 2307 is the closest memorable year after 2018.
So, Sudipta should wait about 2307-2018 = 289 years only. got it?
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