Forgot password? New user? Sign up
Existing user? Log in
If I have the 5 colored shapes shown that I can rotate, and I use each shape once, is it possible to place them so they fit perfectly in a 5×4 rectangle?
Hint: Notice the checkerboard pattern of the rectangle, and consider how the shapes would be colored if they followed the same pattern.
Are you sure you want to view the solution?
Suppose you have two identical plastic bowls: bowl A and bowl B. Bowl A is empty, while bowl B is filled with room temperature water. If you place an identical ice cube in each bowl, which bowl's ice cube will melt first?
Are you sure you want to view the solution?
Friends Stella and Robert each have a ball of the same size, except Stella's ball is made of steel, while Robert's is rubber. They are having a competition to see who can launch their ball farthest. If they each have a cannon capable of accelerating their ball to 50 m/s at the same angle of projection, who will win?
Details and Assumptions:
Are you sure you want to view the solution?
A copies of 3232+32+⋯+3220≤A+BA+B=B copies of 5454+54+⋯+54≤24=?
I have A copies of 32 on the left-hand side of the equality, and B copies of 54 on the right. In total, I've written down between 20 and 24 fractions. Exactly how many fractions are there?
Are you sure you want to view the solution?
The birthday paradox is a surprising result of probability. Suppose you randomly chose 23 people and put them in a room. Then there would be a good chance (greater than 21) that two of those people share a birthday (even though there are 365 days in the year).
What about birth seasons (spring, summer, fall, winter)? Suppose you randomly chose 3 people and put them in a room. Then is it true that there would be a greater than 21 chance that two of them share a birth season?
Note: Birth seasons do not all have the exact same likelihood. However, their likelihoods are close enough that you can assume they are equal for this problem.
Are you sure you want to view the solution?
Problem Loading...
Note Loading...
Set Loading...