BMAD

There is a solution but I find it unsatisfactory. Using kinematics we can set up a system and find two solutions though one doesn't make sense.

lol, i meant to make the rods' diameter 2in not the radii

I am pretty sure bonanova asked a variation of this question but I can't seem to locate it... Anyways: Suppose there is a Ferrari and a truck on a collision course. They will crash in two hours.The truck is going 60mph and the Ferrari is going 80mph. There is also a magical fly on the Ferrari. When the two hour time began the fly instantly achieved and maintained its maximum speed. The fly flew to the truck and back and to the truck and back. Upon the returning from the second trip, the fly, the truck, and the Ferrari all collide. How fast was the fly going?

Suppose that you have 3 rods that have a radius of 2in and a length of 6in. If they were dropped in a square-based box with a length of 7in, what is the probability that none of the rods touch? You can assume that the two rods would not roll once they came in contact with the box and that the rods always landed flat in the box.

It is purposefully directed but not meant to imply that there is a different result.

What is the probability that you could pick at random from the rational numbers a number that contains the string ....7777777..... (the string of six 7's need only to exist consecutively while other digits can occur in the number)?

I have

Player 1 has a 6x6 grid With rows numbered 1 - 6 Player 2 has a 1x6 grid with columns numbered 1-6. Player One begins by filling in the first horizontal row of her table (row 1) with a run of X’s and O’s. That is, on the first line of her board, she will write six letters – one in each box – each letter being either an X or an O. Player Two looks at Player One’s first row and then places either one X or one O in the first box of her board. So at this point, Player One has filled in the first row of her board with six letters, and Player Two has filled in the first box of her board with one letter. The game continues with Player One noticing what Player Two placed on her board and then writing down a run of six letters (X’s and O’s), one in each box of the second horizontal row of her board, followed by Player Two writing one letter (an X or an O) in the second box of her board. This game proceeds in this fashion, with each player’s moves visible to the other, until all of Player One’s boxes are filled with X’s and O’s; thus, Player One has produced six rows of six marks each, and Player Two has produced one row of six marks. Player One wins if any horizontal row she wrote down is identical to the row that Player Two created. Player Two wins if Player Two’s string is not one of the six strings made by Player One. Would you rather be Player One or Player Two?

Each of the 9 referees on the figure skating championship estimates the program of 20 sportsmen by assigning him a place (from 1 to 20). The winner is determined by adding those numbers. (The less is the sum - the higher is the final place). It was found, that for the each sportsman, the difference of the places, received from the different referees was not greater than 3. What can be the maximal sum for the winner?

Medians divide the triangle onto 6 smaller ones. 4 of the circles inscribed in those small ones are equal. Prove that the triangle is equilateral.

Consider the following sequence where (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) ... now clearly this is the same as (0) + (0) + (0) + (0) + (0) + (0) ... = 0 however if I apply the associative property of addition to this series I get... 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + (-1 + 1) + (-1 + 1) ... which clearly equals 1 + (0) + (0) + (0) + (0) + (0) ... = 1 But 1 does not 0, is the associative property wrong?

We have a perfect machine for turning a light on and off. First, we have the light on for one minute, after which it is turned off for one half of a minute. Then it is on again for one fourth of a minute and off for one eighth of a minute. This continues with the light turned on or off after one half of the preceding time period. After two full minutes an infinite sequence of offs and ons will have occurred. At this time, will the light be on or off?

I disagree with your numbers but I concede your point. I was doing 2/11 to see that eleven lines wouldn't work when I should have been doing 2/12 to see that dividing the space into 12 areas would.

to be clear, for edges, i mean straight line segments and the plane is 2d.

Suppose there are 6 points in a plane. What is the most amount of edges that could be used to connect the points (without overlapping)? What if there were 7 points? 8 points? n points?

No... with the height of the triangle at .173, this would not work, even in this context.

I have it in a much smaller amount but not as small as our new friend above. My answer is...

care to have your father explain? I have a different solution.

Suppose there is an equilateral triangle (side length 1/5 unit) inside a unit circle. Drawing straight lines through the circle, what is the least amount of lines that it would take to ensure we intersected (found) the triangle?

I hate to bring up my dvds again (My old post about my dvds) but I love movies and so of course i got 6 new dvds for Christmas. Before Christmas , i had 26 dvds in ABC order. With each DvD starting with 1 of 26 letters in the English alphabet. After i put my new 6 dvds up, how many places to the right should i expect my "U" DvD to shift?

Well done!

But that is silly right? One single sample could very well have included individuals that have a higher than average rate. The mean being 15 implies that there is significant distribution above and below 15. So maybe they just sampled from above?