I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses. Here are the seven solutions I've found (on the Internet)...

May 13, 2014 · 1 If a number ends with n n zeros than it is divisible by 10n 10 n, that is 2n5n 2 n 5 n. A factorial clearly has more 2 2 s than 5 5 s in its factorization so you only need to count how many 5 5 …

Jan 30, 2017 · Given that there are $168$ primes below $1000$. Then the sum of all primes below 1000 is (a) $11555$ (b) $76127$ (c) $57298$ (d) $81722$ My attempt to solve it: We know that below …

Finding 2 poisoned bottles of wine out of a 1000 Ask Question Asked 14 years ago Modified 6 months ago

Aug 22, 2017 · How many positive integers less than 1000 1000 divisible by 3 3 with sum of digits divisible by 7 7? Ask Question Asked 8 years, 5 months ago Modified 8 years, 5 months ago

Aug 5, 2019 · 1000 1000 is the number of small cubes in the original cube. Each face of the original cube contains 10 × 10 = 100 10 × 10 = 100 small cubes, so the effect of removing the small cubes …

Jul 17, 2019 · I understand that changing the divisor multiplies the result by that, but why doesn't changing the numerator cancel that out? I found out somewhere else since posting, is there a way to …

A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street. However, if you perform the action of crossing the street 1000 times, then your chance of being ...

Consider all 1000-element subsets of the set A = {1, 2, 3,..., 2015} A = {1, 2, 3,, 2015}. From each such subset choose the least element. The arithmetic mean of all of these least elements is p q p q, where …

Thus, in your problem N3 = ⌊1000 3 ⌋ = 333 N 3 = ⌊ 1000 3 ⌋ = 333, N4 =⌊1000 4 ⌋ = 250 N 4 = ⌊ 1000 4 ⌋ = 250, and so on. There's no problem with numbers near 1000 1000. The calculation that you're …