Given a corked bottle with only a penny inside, how can you remove the penny without pulling out the cork, breaking the bottle and leaving the cork intact?
Farmer Finnegan needs to build a fence to keep his horses on his property. He only has a little over 1.5 miles of fence materials, but there’s also a mile-long straight river running through his property. What shape should he use for the fenced in area to give his horses the most space possible?
Our dear friend Finnegan should build a half-circle fence with the river as the diameter, giving the horses about 0.4 square miles to frolic and play in.
Area of semi-circle = πr2 / 2 = π × .5 miles2 / 2 = 0.3927
You watch a group of words going to a party. A word either enters through one of two doors or is turned away by the guards. ‘HIM’ goes through door number one and ‘BUG’ goes through door number two. ‘HER’ is turned away. ‘MINT’ and ‘WEAVE’ go in through door one, ‘DOOR’ and ‘CORD’ take door two and ‘THIS’ and ‘That’ aren’t allowed in.
What determines whether a word can enter and which door they must use?
Door number one is for words composed entirely of capital letters written using only straight lines, such as A, E, F, H, and I. The entire set of letters allowed through door number one are AEFHIKLMNTVWXYZ. Door number two, as might be expected, is for words with capital letters that have a curve, including BCDGJOPQRSU. Any words composed of both straight and curved letters (or lowercase letters) are not allowed in. The word ‘THAT’ would have been sent through door number one, if the letters had been capitalized.
The problem works out to a set of three equations:
b + c + d = 22
a + c + e = 22
a + b + c + d + e = 30
Solving for c = 14, leaving d = 8 – b and e = 8 – a. In other words, c must be 14, but the other two numbers just have to add up to 8. The requirement that they be unique rules out 4 + 4, so you’re left to choose from the following combations for b + d and a + e:
0 + 8
1 + 7
2 + 6
3 + 5
Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you’re told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Which box should you remove a marble from to determine the contents of all three boxes?
The one labeled both. Since you know it’s labeled incorrectly, it must have all black marbles or all white marbles. After you determine what it contains, you can identify the other two boxes by the process of elimination.
The numbers must be in ascending order. This can be a fun one to have people work out in person, as they test out three-number series and you can tell them whether or not they satisfy the pattern.