Saturday, November 18, 2017

One equals 0.999...


The following is a mathematical proof that 1 is equal to 0.999.... What's wrong with it? Click below for the answer.
$x = 0.999...$
$10x = 9.999...$
$10x = 9 + 0.999...$
$10x = 9 + x$
$9x = 9$
$x = 1$


Saturday, November 11, 2017

Two equals one?


The following is a mathematical proof that two equals one. What's wrong with it? Click below for the answer.
$a = b$
$aa = ab$
$aa - bb = ab - bb$
$(a + b)(a - b) = b(a - b)$
$a + b = b$
$a + a = a$
$2a = a$
$2 = 1$


Saturday, November 4, 2017

State Names


There's only one letter in the English alphabet that is not used in the name of any of the 50 United States. Do you know which letter it is? Click below for the answer.



Saturday, October 28, 2017

Tic-Tac-Toe


In a standard game of Tic-Tac-Toe, players take turns placing X's and O's on a 3x3 grid until one player makes three-in-a-row in any direction (horizontally, vertically, or diagonally). Because of these rules, you can only place a maximum of five of either symbol on the board during a game, often ending in a draw.

Can you place six X's on a Tic-Tac-Toe board without making three-in-a-row in any direction? (Without placing any O's.) Click below for the solution.




Saturday, October 21, 2017

Draw Two


Two numbers are drawn at random from the integers 1 through 10. What is the expected value of their sum? Does it change if the second draw is done with or without replacement? Click below for the answers.


Saturday, October 14, 2017

Chicken McNuggets


You drove for hours last week to get your hands on McDonald's limited edition Szechuan sauce, and now you need some chicken nuggets for you and all of your friends. You can buy McNuggets in boxes of 6, 9, and 20. What is the largest whole number of nuggets that it is not possible to obtain by purchasing some combination of boxes of 6, 9, and 20? Click below for the answer.




Saturday, October 7, 2017

Pennies


Would you rather have a ton of pennies, four miles of pennies lined up end-to-end, or a stack of pennies half a mile tall? Click below for a hint, or for the answer.