Where Does the Z Go?
A E F H I K L M N T V W X Y -------------------------------------------- Z B C D G J O P Q R S U
The Missing Denominators
If $\dfrac{1}{3} = \dfrac{1}{a} + \dfrac{1}{b}$, find the value of $a$ and $b$.
The Missing Numerators
In the below equation, $a$ and $b$ are whole numbers. Find the values of $a$ and $b$. $$\dfrac{a}{11} + \dfrac{b}{3} = \dfrac{31}{33}$$
The Work Crew
A crew of 3 workers needs 3 weeks and 2 days to complete a project. Because the workers have no union protections, adding more workers is not expensive. On the other hand, the capitalists are very aware that “time is money”. They hope to make a faster profit by putting more workers on the project. They offer you a percentage of the increased profit if you can tell them exactly how long it would take a crew of 4 workers to complete the project, each working at the same rate as the original workers.
Counting by Threes
If we count by 3s, starting with 1, the following sequence is created: 1, 4, 7, 10, …. What is the 100th number in this sequence? What is the easiest/smartest way to figure this out?
So Many Ones!
A book has 500 pages numbered 1, 2, 3, and so on. How many times does the digit 1 appear in the page numbers?
The Largest X and Y
$X$ and $Y$ are any two different numbers selected from the first fifty counting numbers (1 through 50 inclusive). What is the largest value that the following equation can equal? $$ \dfrac{X + Y}{X - Y} = $$
The Simplest Fraction
Write the following sum as a simple fraction in lowest terms. $$ \dfrac{1}{1 \times 2} + \dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + \dfrac{1}{4 \times 5} + \dfrac{1}{5 \times 6} = $$
Alternating Glasses
Six glasses are lined up in a row. The first, second, and third are filled with water. The fourth, fifth and sixth are empty. Can you make the filled and empty glasses alternate by moving only one glass?
Sparky and the Six-Digit Wonder
You meet Sparky, and as usual he throws you a mathematical challenge… “Take any three digit number and repeat it to form a six-digit number.” Sparky helpfully warns that to make a true three digit number, the first digit can not be zero. “For example, $345$ becomes $345345$ and $558$ becomes $558558$, but $012$ becomes $12012$, which ain’t a six-digit number!” “Good point,” you concede as you wonder where this is headed.
The Tricky Postmaster
The Postmaster gives four 3¢ stamps and three 4¢ stamps to a customer. Using one or more of these stamps, how many different amounts of postage can the customer make?