50 Question Challenge #15, Math: answers and sources
Spoilers ahead! Play the video first. Here is every answer, the fun fact and the source we checked it against.
Scores: 0-19: Rookie · 20-29: Number cruncher · 30-39: Math whiz · 40+: Human calculator. Don't forget your Couch Wager. Spotted a mistake? Email hello@ahaville.com with the question number.
Level 1: Easy
- 1
Let's start easy. How many zeros are in one million?
6 zeros A billion has 9 zeros, and a trillion has 12.
- 2
How many eggs are in two dozen?
24 “Dozen” comes from an old French word for twelve.
Source: merriam-webster.com/dictionary/dozen · wikipedia.org/wiki/Dozen
- 3
How many inches are in a yard?
36 Since 1959, a yard is exactly 0.9144 meters.
Source: wikipedia.org/wiki/Yard · wikipedia.org/wiki/International_yard_and_pound
- 4
Which day is 10 days after a Monday?
Thursday 10 days is one week plus 3 days.
- 5
What comes next: 2, 4, 8, 16?
32 Double 1 ten times, and you reach 1,024.
Source: wikipedia.org/wiki/Power_of_two
- 6
How many quarts are in a gallon?
4 “Quart” comes from the Latin for “a fourth.”
Source: merriam-webster.com/dictionary/quart · wikipedia.org/wiki/Quart
- 7
How many hours is it from 9 AM to 5 PM?
8 hours Dolly Parton's song “9 to 5” won two Grammys.
- 8
On which date is Pi Day?
March 14 It's also Albert Einstein's birthday.
Source: wikipedia.org/wiki/Pi_Day · congress.gov/bill/111th-congress/house-resolution/224 · wikipedia.org/wiki/Albert_Einstein
- 9
How many sides does a pentagon have?
5 sides The Pentagon has 5 sides and 5 floors above ground.
Source: wikipedia.org/wiki/The_Pentagon · wikipedia.org/wiki/Pentagon
- 10
What is 1 + 2 + 3 + 4?
10 Bowling's 10 pins stand in rows of 1, 2, 3 and 4.
Source: wikipedia.org/wiki/Ten-pin_bowling · wikipedia.org/wiki/Triangular_number
Level 2: Everyday math
- 11
A $40 dinner plus a 20% tip comes to how much?
$48 And no, “tip” doesn't stand for “to insure promptness.”
Source: etymonline.com/word/tip · barrypopik.com/blog/to_insure_promptness_tip_false_etymol...
- 12
You pay for a $6.25 coffee with a $10 bill. What's your change?
$3.75 The $10 bill shows Alexander Hamilton.
Source: uscurrency.gov/denominations/10
- 13
An $80 jacket is 25% off. What do you pay?
$60 “Percent” comes from Latin for “by the hundred.”
- 14
A movie starts at 7:45 PM and runs 2½ hours. When does it end?
10:15 PM Early movie theaters charged a nickel: nickelodeons.
- 15
How many hours are in a week?
168 A 40-hour work week is less than a quarter of it.
Source: wikipedia.org/wiki/Hour · wikipedia.org/wiki/Working_time
- 16
It's noon in New York. What time is it in Los Angeles?
9 AM US railroads started using time zones in 1883.
Source: wikipedia.org/wiki/Time_in_the_United_States · loc.gov/item/today-in-history/november-18
- 17
Your car gets 30 miles per gallon. How far can it go on 12 gallons?
360 miles New US cars must show their mpg on the window sticker.
Source: fueleconomy.gov/feg/label/ · wikipedia.org/wiki/Monroney_sticker
- 18
A recipe needs ¾ cup of sugar. How much for a double batch?
1½ cups One cup is 16 tablespoons.
Source: wikipedia.org/wiki/Cup_(unit) · wikipedia.org/wiki/Tablespoon
- 19
You sleep 8 hours a night. What part of a 24-hour day is that?
A third The CDC says adults need 7 or more hours.
Source: cdc.gov/sleep/about/index.html
- 20
Last one: which of these is worth the most?
8 dimes That's 80¢. The dime is the smallest US coin.
Source: usmint.gov/learn/coins-and-medals/circulating-coins/dime · wikipedia.org/wiki/Dime_(United_States_coin)
Level 3: Quick: times tables
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
Level 4: Trick questions
- 31
A bat and a ball cost $1.10. The bat costs $1 more than the ball. What does the ball cost?
5 cents The bat is then $1.05: together, $1.10.
- 32
A farmer has 17 sheep. All but 9 run away. How many are left?
9 “All but 9” means every sheep except 9.
- 33
A patch of lily pads doubles every day and covers a lake on day 48. On which day did it cover half?
Day 47 It doubles overnight: half on day 47, all on day 48.
- 34
What is 10 + 10 × 0?
10 Multiply first: 10 × 0 = 0, then add 10.
- 35
How many months have at least 28 days?
12 Even February: 28 days, or 29 in a leap year.
Source: wikipedia.org/wiki/Month · wikipedia.org/wiki/February
- 36
5 machines make 5 gadgets in 5 minutes. How long do 100 machines take to make 100 gadgets?
5 minutes Each machine makes one gadget in 5 minutes.
- 37
How many edges does a cube have?
12 edges 6 faces, 8 corners and 12 edges.
Source: wikipedia.org/wiki/Cube
- 38
Divide 30 by ½, then add 10. What do you get?
70 Dividing by ½ doubles it: 60, plus 10.
- 39
A brick weighs 1 pound plus half a brick. What does a whole brick weigh?
2 pounds Half a brick weighs the 1 pound, so the whole weighs 2.
- 40
Last one: multiply all ten digits on a phone keypad. What do you get?
0 One of them is 0, and anything times 0 is 0.
Source: wikipedia.org/wiki/0
Level 5: Impossible
- 41
What is a googol?
1 with 100 zeros A 9-year-old boy named it, in 1920.
Source: wikipedia.org/wiki/Googol
- 42
Which year is MCMLXIX?
1969 The year people first walked on the Moon.
Source: wikipedia.org/wiki/Roman_numerals · nasa.gov/mission/apollo-11/
- 43
Which of these is a prime number?
97 51 = 3 × 17, 57 = 3 × 19 and 91 = 7 × 13.
Source: wikipedia.org/wiki/Prime_number · wikipedia.org/wiki/List_of_prime_numbers
- 44
About how long is a billion seconds?
About 32 years A million seconds is only about 11½ days.
Source: wikipedia.org/wiki/1,000,000,000 · wikipedia.org/wiki/1,000,000
- 45
In how many different orders can 4 people sit on a 4-seat couch?
24 10 people in a line: 3,628,800 orders.
Source: wikipedia.org/wiki/Factorial · wikipedia.org/wiki/Permutation
- 46
What is a dozen dozen called?
A gross That's 144. And 12 gross make a great gross: 1,728.
Source: wikipedia.org/wiki/Gross_(unit)
- 47
What is the golden ratio, to three decimal places?
1.618 Divide 89 by 55, and you get 1.618…
Source: wikipedia.org/wiki/Golden_ratio
- 48
How many times does the digit 9 appear when you write 1 to 100?
20 Ten in the ones place, and ten more in the 90s.
- 49
Which number is spelled with its letters in alphabetical order?
Forty F-O-R-T-Y. And O-N-E is in reverse order!
Source: wikipedia.org/wiki/40_(number)
- 50
The very last one. What do all the whole numbers from 1 to 100 add up to?
5,050 Pair them up: 1 + 100, 2 + 99… 50 pairs of 101.
Source: wikipedia.org/wiki/Triangular_number · wikipedia.org/wiki/Arithmetic_progression
The Big Aha stories
- The state that almost changed pi: A doctor in Indiana claimed he had solved a famous old geometry puzzle. In 1897, a lawmaker turned his idea into a bill. Hidden in the bill's math was a wrong value for pi: 3.2. The real value is about 3.14. Indiana's House of Representatives passed it 67 to 0. By chance, a Purdue math professor was at the statehouse. He explained the problem to some of the senators. The Senate put the bill off, and it never became law. Sources: in.gov/iara/from-the-vault-blog/vault-pi-bill/ · journals.indianapolis.iu.edu/index.php/ias/article/downlo... · wikipedia.org/wiki/Indiana_pi_bill
- The man who said no to a million dollars: In 2000, the Clay Mathematics Institute named seven famous unsolved math problems, with a $1 million prize for each. In 2002 and 2003, a Russian mathematician, Grigori Perelman, posted a proof of one of them, the Poincaré conjecture, on the internet. In 2006, he turned down the Fields Medal, one of the top honors in math. In 2010, the institute awarded him the $1 million. He said no to that, too. It is still the only one of the seven problems that has been solved. Sources: claymath.org/millennium/poincare-conjecture/ · claymath.org/millennium-problems/ · mathunion.org/imu-awards/fields-medal/fields-medals-2006 · wikipedia.org/wiki/Grigori_Perelman
Bonus question
A snail climbs 3 feet up a 10-foot wall each day and slips back 2 feet each night. On which day does it reach the top? We reveal the answer in the pinned comment under the video.