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Reversing the digits

Source: Cono Sur 2008 #1

November 17, 2015
number theorycono sur

Problem Statement

We define I(n)I(n) as the result when the digits of nn are reversed. For example, I(123)=321I(123)=321, I(2008)=8002I(2008)=8002. Find all integers nn, 1≤n≤100001\leq{n}\leq10000 for which I(n)=⌈n2⌉I(n)=\lceil{\frac{n}{2}}\rceil. Note: ⌈x⌉\lceil{x}\rceil denotes the smallest integer greater than or equal to xx. For example, ⌈2.1⌉=3\lceil{2.1}\rceil=3, ⌈3.9⌉=4\lceil{3.9}\rceil=4, ⌈7⌉=7\lceil{7}\rceil=7.
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