Saturday, September 16, 2017

Digit Frequency

If you write down all the numbers from 1 to 1000 (inclusive) which digit occurs most frequently? Which digit appears least frequently in the same range? Click below for the answers.

Saturday, September 9, 2017

Counting Chickens

If one-and-a-half chickens lay one-and-a-half eggs in one-and-a-half days, how many eggs does one chicken lay in one day? Click below for the answer.

Saturday, September 2, 2017

Number Sense

How good is your "number sense"? How many of the following can you answer without using a calculator or looking up a conversion factor?
  1. Are there more inches in a mile, or Sundays in 1000 years?
  2. Are there more seconds in a week, or feet in 100 miles?
  3. Are there more millimeters in a mile, or seconds in a month?
  4. Which is larger, multiplying all the numbers from 1 to 10, or multiplying just the even numbers from 1 to 16?
  5. Which is longer, 666 days or 95 weeks?
  6. Which is longer, 666 inches or 55 feet?
  7. Which is longer, 666 hours or 28 days?
  8. Are there more ounces in a ton or inches in a kilometer?
  9. Which is hotter, $0^{\circ}C$ or $0^{\circ}F$?
  10. Which is larger, $e^\pi$ or $\pi^e$?

Click below for the answers.

Saturday, August 26, 2017

Replacing Marbles

We place 15 black marbles and 15 white marbles in an urn. We have 30 additional black marbles in a bag. Then we follow these rules.

1. Remove two marbles from the urn.
2. If they are different colors, put the white marble back in the urn and the black marble in the bag.
3. If they are the same color, put both marbles in the bag, then put one black marble from the bag into the urn.

Continue following these rules until only one marble is left in the urn. What color is that marble? Click below for the answer.

Saturday, August 19, 2017

Factor Sums

Not counting itself, the number 6 has the factors 1, 2, and 3, which add to 6. The number 28 has the same property (its factors are 1, 2, 4, 7, and 14). Can you come up with a three-digit number that has this property? What about a four-digit number? Click below for the answers.

Saturday, August 12, 2017

Minimum Percentage

75% of men from a certain group are tall, 75% have brown hair, and 75% have brown eyes. What is the minimum percentage that are tall, have brown hair, and have brown eyes? Click below to see the answer.

Saturday, August 5, 2017

A Two-Digit Number

Find a two-digit number that's equal to two times the result of multiplying its digits. Click below to see the answer.