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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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