query: How many multiples of 3 are in $100!$
positive_passages.docid: 27560
positive_passages.text: How many zeroes are in 100!
negative_passages.docid: 102349
negative_passages.text: sum of all the numbers that can be formed using the digits 2,3,3,4,4,4..
negative_passages.docid: 53467
negative_passages.text: Probability of the union of $3$ events?
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 84433
negative_passages.text: Expression generating $\left( \frac{3}{10}, \, \frac{3}{10} + \frac{33}{100}, \, \frac{3}{10} + \frac{33}{100} + \frac{333}{1000}, \dots \right)$
negative_passages.docid: 472
negative_passages.text: In how many ways can $3$ red, $3$ blue, and $3$ green balls be arranged so that no two balls of the same colour are consecutive (up to symmetry)?
negative_passages.docid: 22454
negative_passages.text: How many combinations can I make?
negative_passages.docid: 128538
negative_passages.text: Generate three different random numbers
negative_passages.docid: 128885
negative_passages.text: For 3 numbers represented with $n$ bits in binary, how many bits is required for their product.
negative_passages.docid: 23576
negative_passages.text: Calculating $1+\frac13+\frac{1\cdot3}{3\cdot6}+\frac{1\cdot3\cdot5}{3\cdot6\cdot9}+\frac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $
negative_passages.docid: 13857
negative_passages.text: Why (directly!) does every number divide 9, 99, 999, ... or 10, 100, 1000, ..., or their product?
negative_passages.docid: 127560
negative_passages.text: Question about repeating decimal?
negative_passages.docid: 107742
negative_passages.text: Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
negative_passages.docid: 12250
negative_passages.text: How to find the prime factorization of $100!$.
negative_passages.docid: 149562
negative_passages.text: How many solutions has the equation $\sin x= \frac{x}{100}$ ?
negative_passages.docid: 139776
negative_passages.text: Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
negative_passages.docid: 31485
negative_passages.text: Three negative and three positive $1$s in a serie