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?
One Hundred Days From Now
If today is Monday, what day of the week will it be 100 days from now?
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?
The Very Unknown Value
What is the value of $(x-a)(x-b)(x-c) … (x-z)$?
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