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This Python program runs in 53ms.

Solution:The original number was 9126 (the correct way up).9126 reads as 9216 (= 96²) when inverted.

9126 doubled is 18252, which reads as 25281 (= 159²) when inverted.

We ignore the trivial solution where all numbers are 0, because there is some calculation involved to determine if a number is a perfect square.