Footprints on the Ceiling

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See page 18. If, at the start each glass contains 1 tsp. of liquid, it is obvious that, at the finish, each will hold ½ tsp. of wine and ½ tsp. of water. With 2 tsps. to start, each glass will finally hold 1 1/3 tsps. of its original liquid and 2/3 tsp. of the other. With 30 tsps. the proportion will be 29 1/31 tsps. to 30/31 tsps. If X equals the original amount of liquid the amount of contaminating matter is always X/(X+1)