Nice little trick! A pity to remove the mystery behind it.
If you let your two digit number be 10a+b
then subtract each digit from it,
we get 10a+b-a-b = 9a.
Thus, your result is always a multiple of 9 (i.e. 9, 18, 27, 36, 45 etc).
If you check the table, the multiples of 9 show identical objects e.g. Money Clip. Each time you play the game, the objects are re-shuffled but the multiples of 9 still show identical objects.
Regards, Rob.
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