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 …
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 …
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
Seven balls of different weights are randomly painted red, orange, yellow, green, blue, indigo and violet, each ball being painted a distinct color. The green ball is found to be heavier than the blue ball, and the red ball is found to be heavier than the yellow ball. Given just this information, if the probability …
A natural number a is called a lucky number if the sum of its digits is 7. Arrange all lucky numbers in an ascending order, and we get a sequence a1, a2, a3, …. If an = 2005, compute a5n.
What is the number of ways a tic tac toe game can be ended with a draw? Note: Either ‘O’ or ‘X’ can start first.
63042 Calvin thinks of a 5-digit number. He tells you the product of the digits is n. Knowing only that, there are exactly 200 different numbers which Calvin could have thought of. Find the sum of all possible values of n.