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This is a simple puzzle to solve programatically. The following Python code runs in 36ms. It assumes that the number of metres is a positive integer.

Solution:1683 metres = 1836 yards.A further solution would be 5724 yards = 5247 m. There are many more if we go to larger numbers.

But I have to say it’s a lousy conversion factor. 35 yards = 32 m would be a much closer rule-of-thumb approximation. I haven’t found any “anagram” conversions using four digits or fewer.