BMAD

yes, i meant integer

A game token costs $10 to play. The pay out is $100. You can purchase multiple entries if you desire. For each entry you purchase, you must pick the lowest positive number that no one else picks. If there are ten people, including yourself, seeking to purchase tokens, what is your strategy?

Can you post an example?

yes

Prove that x^(1/x) = x^-x has only one solution

You and four friends are playing Russian roulette, one bullet is in a chamber of a six chamber gun. Each of you must take a shot from the gun. The chamber will only be spun once, before anyone has taken a shot. If you got to chose, which position, 1st, 2nd, 3rd, 4th, or 5th would best help your chances of survival?

is there another?

In front of you is a line and a line segment. You need to dissect the line segment into 6 equal segments. Unfortunately you only possess two skills. you have the ability to mark points and you have the ability to draw straight segments. How will you segment the segment into six equal parts?

Here is a list of months and a code for each January: 7110 February: 826 March: 5313 April: 541 May: 3513 June: 4610 July: 4710 What is the code for the month of August?

For 0<x<y find an integer solution for x^y = y^x

A number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained. For example, 77 has a persistence of four because it requires four steps to reduce it to one digit: 77-49-36-18-8. The smallest number of persistence one is 10, the smallest of persistence two is 25, the smallest of persistence three is 39, and the smaller of persistence four is 77. What is the smallest number of persistence five?

Suppose superman can survive the vacuum of space (the comics are inconsistent with this ability). Let's say he is in the front of a spaceship that just crossed, what I believe in English is called, the event horizon for a black hole. That point where matter gets sucked into hole. Is it possible for superman to move to the rear of the ship and escape the black hole, assuming that the back of the ship hasn't crossed the event horizon?

Find a continuous function where the following identity is true: f(2x) = 3f(x)

How many points would you need to have to uniquely determine an ellipse given that you know a foci is located at (0,0).

I intended your interpretation but came up with a much different answer than the ones reported forgive my lack of parenthesis what I meant for the problem is 1/(2x)

His initial bet is $1250. Every time he wins, he calculates his total and takes 1/4 of it to bet. So initially he has 5000, 5000 x .25 = 1250. If he were to win, he would earn double his bet so he would have $6250. Recalculating he would bet $1562.50. If he loses his bet he would maintain that amount in his next bet. He keeps at it until he is unable to make his desired bet.

Think more logically

Abraham is tasked with reviewing damaged planes coming back from sorties over Germany in the Second World War. He has to review the damage of the planes to see which areas must be protected even more. Abraham finds that the fuselage and fuel system of returned planes are much more likely to be damaged by bullets or flak than the engines. What should he recommend to his superiors?

A gambler has $5,000 and is playing a game of chance with a win probability of .95. Every time he wins, he raises his stake to 1/4, of his bankroll. The gambler doesn't reduce his stake when he loses If he keeps at it, what are his expected winnings?

A town's population of size x doubled after 30 years (2x). How long ago was this population 1/2x?

You are to color a 5x5 square grid using green, red, blue, and yellow. You must color it in a way where a square cannot share a side or a vertex with another square of the same color. What is the fewest amount of yellow squares needed to color this appropriately? Now instead lets divide each square diagonally from the top left corner to the bottom right corner. What is the fewest amount of yellow colorings needed?

If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, P(BB) = (15/21)×(14/20) = 1/2. The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs. By finding the first arrangement to contain over 1012 = 1,000,000,000,000 discs in total, determine the number of blue discs that the box would contain.

? arccos(-1/3) = 109.5 degrees.

Your solution does simplify to something really nice. I will see if anyone sees it before I give it away. Nice work.