ID 861

The speed of light is 3 x 10^{5} kilometers/second.

If the sun is 1.5 x 10^{8} kilometers from Earth, how many seconds does it take light to reach the Earth?

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The North American emergency telephone number is 911.

How many three-digit integers are exactly 911 more than a two-digit integer?

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The date July 31, 1370 in MM/DD/YYYY format is a palindrome that may be read the same way in either direction (the same forwards as backwards).

07/31/1370

How many such dates are there from June 1, 1352 to June 1, 2012?

ID 2212

We use the decimal number system with base 10.

The binary numeral system (base 2) is widely used for digital computations.

In a number system, 17 is a prime number.

A prime number is a positive integer that has no positive divisors other than 1 and itself.

What is the base of the number system?

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ID 2274

Make 33 by using three 3s and any math operators.

How many times do you use the plus sign (+) in the expression?

ID 2277

The sum of two prime numbers is equal to 888.

There are several options. We look for two numbers with maximum product.

What is one of the numbers?

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ID 3191

The typical healthy resting heart rate in adults is 60–80 beats per minute.

If you live 80 years, how many times will your heart beat?

ID 3536

Pairs of primes separated by a single number are called prime pairs. Examples are 809 and 811.

The number between a 3-digit prime pair is always divisible by:

ID 3539

Find the last 3 digits of the sum of

1 + 11 + 111 + . . . + 111 . . . 111,

where the last number has 99 ones.

ID 3591

A number is palindromic, if it is the same backwards as forwards.

Of the largest palindrome made from the product of two two-digit numbers, find one of the numbers.

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ID 3946

You can throw an unlimited number of darts at the dartboard.

Some total scores are impossible to obtain, such as all the numbers less than 5 as well as 6, 8, and 9.

What is the highest whole number score that is impossible to obtain?

The Dart Problem by Bill Graham in Games Magazine (August 2003)

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ID 4045

If the sum of three distinct positive integers is 33, what is the maximum possible product of the numbers?

ID 4340

The product of two integers is 1000.

Neither of the numbers contains a zero.

Find the sum of the integers.

ID 4684

What is a mystery number if you add it to 1, then multiply by 2, then add 3, then multiply by 4, you get 5?

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The product of 99 integers is 99.

What is the largest possible value the sum of the numbers can have?

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ID 5030

What is the smallest 7-digit prime number?

A prime number is a natural number that has no positive divisors other than 1 and itself.

ID 5169

Leslie Green asks:

Find the ratio A/B where A is the number of elements in the set of all positive integers

and B is the number of elements in the set of all even positive integers.

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The product of real positive numbers a, b, c, and d is equal to 1.

What is the minimum value of their sum?

ID 5267

The sum of the digits of a four-digit number is 15.

All the digits are different and they are in decreasing order.

Each digit is a power of 2.

What is the sum of the first two digits?

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{ Positive Odds } = { 1, 3, 5, 7, 9, 11, … }

How many positive integers less than 100 have only odd digits?

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What is the units digit of the product of all positive two-digit integers which are evenly divisible by 11?

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Binary 11 means 1x2^{1} + 1x2^{0} = one two and one one.

101 is 1x2^{2} + 0x2^{1} + 1x2^{0} = 4 + 0 + 1 = 5 (decimal number system).

When the number 2017 is written in the binary system, how many digits will it have?

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ID 6727

This sequence of numbers repeats so they could be written in a circle (after deleting the 1 and 6 at the end, since they just show the repeat point).

There is a definite mathematical rule to go from one number to the next.

1, 6, 4, 3, 0, 5, 3, 1, 6, . . .

Sadly one (and only one) of the numbers has been mis-typed, but which one?

Author: Leslie Green

ID 6955

What is the largest possible remainder that can be obtained when a two-digit number is divided by the sum of its digits?

ID 7071

Which row contains both the square of a positive integer and the cube of a different positive integer?

This is a typical SAT question.