## Sum of Squares

If x is an even integer that can be written as the sum of two perfect squares, prove that x / 2 can also be written as the sum of two perfect squares.

If x is an even integer that can be written as the sum of two perfect squares, prove that x / 2 can also be written as the sum of two perfect squares.

What is a special property or feature that all of the following words have in common? assess, banana, dresser, grammar, potato, revive, uneven, voodoo

What common word or phrase is this rebus referring to? ♣ OFFICE♠ SCHOOL♥ HOME♦ STORE

Hasan and Lauren attended a dinner party with 4 other couples. Since some people already knew some of the other guests, every person at the dinner party shook hands with every person they had not met before. Lauren noticed that…

Which logical statement(s) below must be correct? Exactly one statement on this list is incorrect Exactly two statements on this list are incorrect Exactly three statements on this list are incorrect Exactly four statements on this list are incorrect Exactly…

What common word or phrase is this rebus referring to? GIVE GIVE GIVE GIVEGET GET GET GET

After the results of an election, you are told that one candidate has received the majority of the votes, but you don’t know which candidate. You have exactly one opportunity to hear the votes, but: The list of votes is…

Abe, Ben, and Catelyn were playing 1-on-1 tennis matches one afternoon. After each match, the winner stayed on the court and the loser was replaced by the person who sat out. At the end of their session, Abe had played…

There is a standard deck of cards, with some cards face-up and the rest of the cards face-down. You are told exactly how many cards are face-up, but you are not allowed to look at the cards. Without seeing which…

What common word or phrase is this rebus referring to? T O U K E E P C H

You spend an entire day hiking up a mountain, and camp overnight at the top. The next day, you hike down the mountain along the same trail, starting around the same time you started the day before. How likely is…

A blind man has to take exactly one green pill and one blue pill each day – no more and no less. However one day he accidentally takes out two pills from the green bottle and two pills from the…

There are two trains that run between two cities. The trains are identical and run on identical routes, so passengers have no preference between the two and would take whichever train that pulls into the station. The trains run at…

You are trying to hit a moving battleship, but you have no way of monitoring its position. However, you have the following information: You know where the battleship started. You know when the battleship started moving. You know the battleship…

Which English word can be added to either the beginning or end of each of the following words, in order to create four valid English words? ONE ACT KIND SPA

You have two odd hourglasses: one that times exactly 4 minutes and one that times exactly 7 minutes. What is the best way to measure exactly 9 minutes using just these two hourglasses?

Simpson’s Paradox (also sometimes known as the reversal paradox or Simpson’s reversal) refers to the phenomenon in which a trend or result that appears in multiple groups of data no longer appears—or in fact reverses—when the groups are combined.

Which perfect square of a 4-digit number has the same last four digits as the original number?

There are 362,880 different ways to arrange the digits 1 through 9 into a 9-digit number. How many of these combinations are prime numbers?

A bicycle shop has some number of unusual bicycles. All their bikes are identical (there’s more than one bike), and each bike’s front and back wheels has at least one spoke each (each bike has more than one spoke). You…

What is black when you buy it, red when you use it, and gray when you throw it away?

There are three playing cards in a row. There is a heart to the left of a diamond. There is a five to the right of a jack. There is a club to the left of a diamond. There is…

You have 5 short chains of 3 links each, that you would like to connect into one long 15-link chain. To connect links, you need to cut open a link, join it with another link, and then close it. What…

A pretty challenging chess puzzle, because there isn’t a pre-determined number of moves. White to play and force a draw.

Which is the odd one out? catwoman deus ex machina parishioner pyromania scuba