Our minds constantly look for shortcuts. That is useful in everyday life, but those same shortcuts can lead to quick and wrong answers. These games exploit linguistic ambiguity, mathematical habits and small lapses of attention. Try to answer each question quickly, then reveal the result and explanation.
The 50 questions
How many times does the digit 7 appear from 1 to 100?
Show result and explanation
Result: 20.
Explanation: It appears ten times in the units place and ten times in the tens place. In 77 it appears twice, as it should.
How many months have 28 days?
Show result and explanation
Result: 12.
Explanation: Every month has at least 28 days, not just February.
A farmer has 17 sheep. All but 9 run away. How many remain?
Show result and explanation
Result: 9.
Explanation: “All but 9” means that 9 did not run away.
If you overtake the runner in second place, what place are you in?
Show result and explanation
Result: Second.
Explanation: You take the place of the runner who was second, not the leader’s place.
How many times can you subtract 10 from 100?
Show result and explanation
Result: Once.
Explanation: After the first subtraction you are subtracting 10 from 90.
A doctor gives you 3 pills and says to take one every 30 minutes. How long does it take to take them all?
Show result and explanation
Result: 1 hour.
Explanation: Take the first immediately, the second after 30 minutes and the third after 60.
You have a match, a candle and an oil lamp. What do you light first?
Show result and explanation
Result: The match.
Explanation: You need it to light the candle or lamp.
A rooster lays an egg on a roof. Which way does it roll?
Show result and explanation
Result: It does not.
Explanation: Roosters do not lay eggs.
How many animals of each kind did Moses take on the ark?
Show result and explanation
Result: None.
Explanation: The person with the ark was Noah, not Moses.
If 5 machines make 5 objects in 5 minutes, how long do 100 machines take to make 100 objects?
Show result and explanation
Result: 5 minutes.
Explanation: Each machine makes one object in 5 minutes; 100 machines work in parallel.
A father and son are 66 years old together. The father is 60 years older than the son. How old is the son?
Show result and explanation
Result: 3 years old.
Explanation: If the son is x years old, the father is x + 60: 2x + 60 = 66, so x = 3.
A plane crashes exactly on the border between Italy and France. Where are the survivors buried?
Show result and explanation
Result: Nowhere.
Explanation: The survivors are alive.
You have 6 apples and take 4. How many apples do you have?
Show result and explanation
Result: 4.
Explanation: You have the four apples you took.
A man goes out in the rain without an umbrella or hat, yet not one hair gets wet. Why?
Show result and explanation
Result: He is bald.
Explanation: He has no hair to get wet.
Which word is always spelled “wrong” in the dictionary?
Show result and explanation
Result: “Wrong”.
Explanation: It is wordplay: the dictionary contains the word “wrong”, spelled correctly.
An electric train travels north. Which way does its smoke blow?
Show result and explanation
Result: Nowhere.
Explanation: An electric train does not produce steam-engine smoke.
Two fathers and two sons go fishing and catch three fish. Each takes one home. How is that possible?
Show result and explanation
Result: They are three people.
Explanation: A grandfather, his son and his grandson: the middle person is both father and son.
What is half of 2 plus 2?
Show result and explanation
Result: 3, if “half of 2” is calculated first.
Explanation: Half of 2 is 1, and 1 + 2 = 3. Without parentheses, the words could also mean half of (2 + 2), which is 2.
What is 2 + 2 × 2?
Show result and explanation
Result: 6.
Explanation: Multiplication comes before addition: 2 + 4 = 6.
If a brick weighs 1 kg plus half a brick, how much does a brick weigh?
Show result and explanation
Result: 2 kg.
Explanation: If x is its weight, x = 1 + x/2; therefore x/2 = 1 and x = 2.
A bottle and its cap cost €1.10 together. The bottle costs €1 more than the cap. How much is the cap?
Show result and explanation
Result: €0.05.
Explanation: If the cap costs x, the bottle costs x + 1: 2x + 1 = 1.10, so x = 0.05.
If today is Monday, what day will it be in 100 days?
Show result and explanation
Result: Wednesday.
Explanation: Dividing 100 by 7 leaves a remainder of 2: two days after Monday.
How many times does the digit 1 appear from 1 to 100?
Show result and explanation
Result: 21.
Explanation: Ten times in the units place, ten in the tens place and once in 100. In 11 it is counted twice.
How many digits are needed to write all the numbers from 1 to 10?
Show result and explanation
Result: 11 digits.
Explanation: Numbers 1 through 9 need nine digits in total; 10 needs two more.
What comes next: 1, 11, 21, 1211, 111221…?
Show result and explanation
Result: 312211.
Explanation: Each term describes the digits of the previous term: 111221 reads “three 1s, two 2s, one 1”.
If 3 cats catch 3 mice in 3 minutes, how many cats are needed to catch 100 mice in 100 minutes, assuming a constant average rate?
Show result and explanation
Result: 3 cats.
Explanation: On average three cats catch one mouse per minute, hence 100 in 100 minutes. This is an average-rate model; if catches occurred rigidly only at minutes 3, 6, 9… the timing and rounding would need to be specified.
A snail climbs 3 metres by day and slips 2 metres by night. How many days does it take to climb a 10-metre wall?
Show result and explanation
Result: 8 days.
Explanation: At the start of day eight it is 7 metres up; it climbs 3 and reaches the top before slipping back.
A box contains 10 black socks and 10 white socks. In the dark, how many must you take to guarantee a pair of the same colour?
Show result and explanation
Result: 3.
Explanation: In the worst case the first two are different colours; the third completes a pair.
How many eggs can you eat on an empty stomach?
Show result and explanation
Result: One.
Explanation: After the first egg your stomach is no longer empty.
A clock chimes 6 times in 5 seconds. How long does it take to chime 12 times?
Show result and explanation
Result: 11 seconds.
Explanation: Six chimes have five one-second intervals; twelve have eleven.
If you were 15 yesterday and will be 18 next year, how is that possible?
Show result and explanation
Result: Today is January 1 and your birthday is December 31.
Explanation: Yesterday, December 31, you turned 16: before your birthday you were 15. You will turn 17 this year and 18 next year.
Which is heavier: 1 kg of iron or 1 kg of feathers?
Show result and explanation
Result: They weigh the same.
Explanation: A kilogram is a kilogram, whatever the material.
A man has 4 daughters. Each daughter has a brother. How many children does he have altogether?
Show result and explanation
Result: 5.
Explanation: All four daughters can have the same brother.
Three doctors say that Luke is their brother. Luke says he has no brothers. How is that possible?
Show result and explanation
Result: The three doctors are his sisters.
Explanation: Luke has no male siblings, but he has three sisters.
A man looks at a portrait and says: “I have no brothers or sisters, but this man’s father is my father’s son.” Who is in the portrait?
Show result and explanation
Result: His son.
Explanation: Since he has no siblings, his father’s son is himself; he is therefore the father of the person in the portrait.
How many letters are in the alphabet?
Show result and explanation
Result: 8 in the word “alphabet”.
Explanation: This playful reading counts the letters of the word “alphabet”. If the question means the English alphabet itself, the answer is 26.
What always increases and never decreases?
Show result and explanation
Result: Your age.
Explanation: Time since birth does not run backwards.
What can you break without touching it?
Show result and explanation
Result: A promise.
Explanation: “Break” is used figuratively.
What gets wetter as it dries?
Show result and explanation
Result: A towel.
Explanation: As it absorbs water from what it dries, the towel gets wet.
What has cities but no houses, rivers but no water, and mountains but no trees?
Show result and explanation
Result: A map.
Explanation: It depicts these places without physically containing them.
What has a head and a tail but no body?
Show result and explanation
Result: A coin.
Explanation: “Heads” and “tails” name its two sides.
What has many keys but opens no doors?
Show result and explanation
Result: A piano.
Explanation: Its keys are musical keys, not keys for locks.
What has a neck but no head?
Show result and explanation
Result: A bottle.
Explanation: “Neck” also names the narrow part of a bottle.
What has four legs but cannot walk?
Show result and explanation
Result: A table.
Explanation: Its “legs” support the furniture.
What goes through a window without breaking it?
Show result and explanation
Result: Light.
Explanation: It passes through transparent glass.
The more you take away, the bigger it gets. What is it?
Show result and explanation
Result: A hole.
Explanation: Removing earth makes the cavity larger.
A man is born in 2000 and dies in 1995. How is that possible?
Show result and explanation
Result: The dates could be years BC.
Explanation: In BC numbering, 2000 BC comes before 1995 BC. The numbers might also refer to rooms or addresses.
A bus starts with 10 passengers. At the first stop 3 get off and 5 get on. At the second, 4 get off and 2 get on. How many people are on the bus?
Show result and explanation
Result: 10 passengers; 11 people including the driver.
Explanation: The final number of passengers is 10 − 3 + 5 − 4 + 2 = 10. The driver is one more person.
A candle is 20 cm tall and burns down by 2 cm per hour. After how many hours is it 10 cm tall?
Show result and explanation
Result: 5 hours.
Explanation: To lose 10 cm at 2 cm per hour takes 10 ÷ 2 = 5 hours.
A mother has 4 daughters: North, South and East. What is the fourth daughter’s name?
Show result and explanation
Result: It is not specified.
Explanation: “West” is the intuitive completion of the list, but the question never says that is her name.