You drove for hours last week to get your hands on McDonald's limited edition Szechuan sauce, and now you need some chicken nuggets for you and all of your friends. You can buy McNuggets in boxes of 6, 9, and 20. What is the largest whole number of nuggets that it is not possible to obtain by purchasing some combination of boxes of 6, 9, and 20? Click below for the answer.

There might be cleverer solutions to this problem, but we can do this fairly easily by listing combinations. Once we hit a streak of six numbers in a row that we can obtain, we know that the last number we couldn't obtain before the streak is the largest such number. Beyond that streak of six we can just add one or more boxes of 6 nuggets to one of those numbers to obtain any higher number. (There may be other combinations to obtain some of these numbers, but we only need one combination for each.)

Number

Boxes

1

Not Possible

2

Not Possible

3

Not Possible

4

Not Possible

5

Not Possible

6

6

7

Not Possible

8

Not Possible

9

9

10

Not Possible

11

Not Possible

12

6 + 6

13

Not Possible

14

Not Possible

15

6 + 9

16

Not Possible

17

Not Possible

18

9 + 9

19

Not Possible

20

20

21

6 + 6 + 9

22

Not Possible

23

Not Possible

24

6 + 9 + 9

25

Not Possible

26

20 + 6

27

9 + 9 + 9

28

Not Possible

29

20 + 9

30

6 + 6 + 9 + 9

31

Not Possible

32

6 + 6 + 20

33

6 + 9 + 9 + 9

34

Not Possible

35

6 + 9 + 20

36

9 + 9 + 9 + 9

37

Not Possible

38

9 + 9 + 20

39

6 + 6 + 9 + 9 + 9

40

20 + 20

41

6 + 6 + 9 + 20

42

6 + 9 + 9 + 9 + 9

43

Not Possible

44

6 + 9 + 9 + 20

45

9 + 9 + 9 + 9 + 9

46

6 + 20 + 20

47

9 + 9 + 9 + 20

48

6 + 6 + 9 + 9 + 9 + 9

49

9 + 20 + 20

That's six in a row, so we can get any higher number of nuggets just by adding boxes of 6 to those combinations. That means that 43 is the largest number of Chicken McNuggets that you cannot buy by combining boxes of 6, 9, and 20.

Would you rather have a ton of pennies, four miles of pennies lined up end-to-end, or a stack of pennies half a mile tall? Click below for a hint, or for the answer.

One penny weighs 2.500 grams (according to the U.S. Mint).
There are about 28.35 grams in an ounce
There are 16 ounces in a pound.
There are 2,000 pounds in a (U.S.) ton.

One penny is 0.750 inches in diameter.
There are 12 inches in a foot.
There are 5,280 feet in a mile.

One penny is 1.52 millimeters thick.
There are 25.4 millimeters in an inch.

Four miles of pennies lined up end-to-end would be $3,379.20, while one ton is $3,628.80, so between the first two options you would be better off to take the ton. However, a stack of pennies half a mile tall would be $5,293.89, so the stack is by far the best option.

Here's a freaky coincidence about World War II. If you add up the year of birth, age in 1944, year of taking power, and the number of years in office in 1944 for each of the five main leaders of the Western world during World War II, the sums are all the same.

Churchill

Hitler

Mussolini

Roosevelt

Stalin

Year of birth

1874

1889

1883

1882

1878

Age in 1944

70

55

61

62

66

Took power

1940

1933

1922

1933

1922

Years in office

4

11

22

11

22

Sum

3,888

3,888

3,888

3,888

3,888

Can you explain this coincidence? Click below for the answer.

There's really no coincidence at all. If you take any person's year of birth and add their age in 1944, the sum will be... 1944. This also goes for the year a leader took office and the number of years they had held office in 1944, so the sum of all four values will always be 1944 + 1944 = 3888. You can make your own puzzle using any year as a reference point.

See the image below of a square inscribed inside a circle inscribed inside a square. If the outer square has an area of 100 square inches, is there a quick way of figuring out the area of the inner square? Click below for the answer.

Spin the inner square around so the corners touch the top, bottom, and sides of the outer square.

Now imagine taking each corner of the outer square and folding them in so they touch in the center of the image. It's easy to see that the area outside the inner square will perfectly cover the area inside, so the inner square has exactly half the area of the outer square, or 50 square inches.

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.

You could write all the numbers down or write a program to count the digit frequencies, but this problem is much easier if you look for a pattern. The digits 0 through 9 all appear the same number of times in the ones place, but 1 through 9 appear a lot more often in the tens and hundreds place (because of numbers like 22, 222, etc., and the fact that we don't write leading 0s). This means that 0 is the least frequent digit. It only appears 192 times in the specified range. What about the most frequent? The digits 1 through 9 appear with exactly the same frequency in the range 1 to 999 (300 times each), so that extra occurrence (in the number 1000) makes 1 the most frequent digit from 1 to 1000.

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

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 $32^{\circ}F$