## 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.

For many people, the intuitive answer is one egg, but it pays double-check your math on this kind of problem. The daily rate of eggs per chicken per day is given by the formula

daily rate = eggs / (chickens x days)

Plugging in the numbers from the first part of the problem, we get

daily rate = 1.5 / (1.5 x 1.5)

daily rate = 1.5 / 2.25

daily rate = 2/3

So, one chicken lays two-thirds of an egg in one day.

daily rate = eggs / (chickens x days)

Plugging in the numbers from the first part of the problem, we get

daily rate = 1.5 / (1.5 x 1.5)

daily rate = 1.5 / 2.25

daily rate = 2/3

So, one chicken lays two-thirds of an egg in one day.

## 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?

- Are there more inches in a mile, or Sundays in 1000 years?
- Are there more seconds in a week, or feet in 100 miles?
- Are there more millimeters in a mile, or seconds in a month?
- Which is larger, multiplying all the numbers from 1 to 10, or multiplying just the even numbers from 1 to 16?
- Which is longer, 666 days or 95 weeks?
- Which is longer, 666 inches or 55 feet?
- Which is longer, 666 hours or 28 days?
- Are there more ounces in a ton or inches in a kilometer?
- Which is hotter, $0^{\circ}C$ or $0^{\circ}F$?
- Which is larger, $e^\pi$ or $\pi^e$?

Click below for the answers.

- Inches in a mile. (63,360. There can be up to 52,178 Sundays in 1000 years.)
- Seconds in a week. (604,800, compared to 528,000 feet in 100 miles.)
- Seconds in a month. (Even if the month only has 28 days, that's 2,419,200 seconds, compared to only 1,609,340 millimeters in a mile.)
- Just the even numbers from 1 to 16. (Multiplying all the numbers from 1 to 10 gives you 3,628,800. Multiplying the even numbers from 1 to 16 give you 10,321,920.)
- 666 days. (95 weeks is only 665 days.)
- 666 inches. (55 feet is 660 inches.)
- 28 days (which is 672 hours).
- Inches in a kilometer. (39,370.1, compared to 35,840 ounces in a long ton, which is the heaviest ton.)
- $0^{\circ}C$ is "hotter" since it is equal to $32^{\circ}F$
- $e^\pi$ (23.14) is larger than $\pi^e$ (22.46).

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