Reu 2006
نویسنده
چکیده
Like every positive integer, the number 19 possesses some fascinating properties. For example, 19 is the smallest prime that is equal to the product of its digits plus the sum of its digits; 19 = 4! − 3! + 2! − 1!; 19 times its reversal (91) is the famous Hardy-Ramanujan number 1729; the sum of 19 consecutive Fibonacci numbers starting from the 19 Fibonacci number is prime; 19 is the smallest prime whose reversal is composite; and 19 is the smallest score it is impossible to obtain in a hand of cribbage. In this paper, we investigate another interesting, and unexpected, property of 19 that even though configurations exist in the Hausdorff metric geometry in which there are k elements at each location between end sets for k equal 1-18 (and for infinitely many different values of k), there is no configuration with exactly 19 elements at each location between the end sets.
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