Subject: mysteries in math Dear Ladies and/or Gentlemen: The below listed question is one from a special friend of mine as a point to ponder and solve. However i do not understand the question. If i did, i could possibly tell you what level of math this is. Most likely it is elementary if i think about it long enough. My request of you is not that you solve the problem, rather you explain to me How to solve this. Thanking you in advance for your assistance and education. Sincerely, Martyanne "In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is __, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __." Each blank is to be filled with a numeral of one or more digits, written in decimal notation. Hi Martyanne, Perhaps it is best to show you a naive attempt at a solution: "In this sentence the number of occurrences of 0 is ..." Well, so far I count one 0 in the sentence, so I put in a 1 in the first blank. With this blank filled, the sentence becomes: "In this sentence the number of occurrences of 0 is 1, the number of 1 is __, of 2 is __, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __." Now with the first blank filled, the number of 1's is two, so I fill in the second blank with 2: "In this sentence the number of occurrences of 0 is 1, the number of 1 is 2, of 2 is __, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __." So far, so good; now there are two 2's in the sentence, so I put in a 2 in the third blank: "In this sentence the number of occurrences of 0 is 1, the number of 1 is 2, of 2 is 2, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __." And I continue in the same way... Oops! Wait a minute. There is something wrong: the number of 2's in the sentence is now 3, not 2. So perhaps I should correct it: "In this sentence the number of occurrences of 0 is 1, the number of 1 is 2, of 2 is 3, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __." But now it is wrong again: the number of 2's is now back to two. Well, perhaps that filling in the other blanks will make another 2 appear, so that the sentence will be right again. That is the point of the problem: Try to fill all the blanks and end up with a sentence that correctly states the number of 0's, 1's, ..., 9's in it. Cheers, Claude Go to Math Central