Use numbers 0, 1, 2, 3, 4, 5 to create none-repeating four-digit numbers. If we call the number with every digit smaller than the one on its left “descending number“, what is the probability for the four-digit number to be a “descending number”.
Our friend Mac likes to eat ice-cream so much that he started to work in an ice-cream parlor. Satisfied by his work, the ice-cream owner gave him 10 different kind of ice-cream each 2 in quantity(20 ice-creams in total). Mac have gone crazy so much that he brought a fair 10 sided dice and devised …
This problem’s question: What is the ratio of the standard deviation of rolling three such dice and selecting the second highest value and the standard deviation of rolling just one die? For this problem, imagine rolling these three dice. The procedure to determine the second highest value is to sort the rolled values into descending …
You are playing a game with a fair six-sided die. If you roll a number greater than 1, then you win that many gold coins. For example, if you roll a 5, then you win 5 gold coins. If you roll a 1, then you lose half of your money. You start this dice game …
The square base of a right pyramid has sides of integral length. The height of the pyramid is also an integer. The volume of the pyramid, which is also an integer, is equal to it’s total surface area. What is the height of the pyramid?
Let S be the set of all 10-digit numbers (which by definition may not begin with 0) in which each digit 0 through 9 appears exactly once. For example, the number 3820956714 is in S. A number n is picked from S at random. What is the probability that n is divisible by 11? If …
Let n be an integer randomly chosen in the interval [1, 120], and consider the sum Sn = sum of (k) from k=1 to k=n. Sn is Least likely to be divisible by _______?
floor(12/2017), floor(22/2017), floor(32/2017), …, floor(20172/2017) How many distinct numbers are there in the list of numbers above?
In the land of Mathematica, a remote tribe made totem poles out of square-heads and big-heads (which were twice as tall as square heads). The square-heads were made of pine, whereas the big-heads were made of ash or birch. The heads were stacked upright to form these totem poles. Find the number of different totem …
Write down all the integers 1 to 1,000,000 in a row. Cross out all of the odd numbers. Of the remaining numbers, cross out all of those that are now in even positions (i.e. cross out 4, 8, 12, 16, …). Of the remaining numbers, cross out all of those that are now in odd …
How many triples of positive integers (r, s, t) such that r < s < t which satisfy the equation below? r + s + t = 52