Trick questions

A trick question is not hard maths. It is a question where the fast answer and the right answer are different. In a study published in 2005, the researcher Shane Frederick asked more than 3,000 people, most of them university students, three short questions. One of them was the bat and the ball below. Most people got at least one of the three wrong. The maths was easy; the fast answer was the problem. The good news is that there is a simple habit that beats almost every trick question: read every word, and check your answer against the story.

A habit that beats trick questions

1. Read the question slowly, all the way to the end.
2. Find the small words that change the meaning: "but", "more than", "half", "you", "now".
3. Ask: what exactly is the question asking for? Not what it looks like it asks.
4. When you have an answer, put it back into the story and check that every sentence is still true.

All but

"All but 9" means all except 9. So if a farmer has 17 sheep and all but 9 run away, then 9 sheep did not run away. There are 9 left. The number 17 is there only to make you subtract.

Who has what, and where are you

There are 7 apples on a table, and you take 3. How many apples do you have? You have the 3 you took. The other 4 are still on the table. The question asks about you, not about the table.

Races work the same way. If you pass the runner in 2nd place, you take their place. You are now 2nd, not 1st: the runner in 1st place is still in front of you. Each time you pass someone, you move up one place. Each time someone passes you, you move down one place.

Questions that hide the answer in plain sight

Which is heavier, 1 kg of feathers or 1 kg of iron? They weigh the same: both weigh 1 kg. The feathers take up much more space, and that is what makes people say "the iron". But the question is about weight, and the weight is written in the question.

Tom's mother has three children. Two of them are Ana and Ben. What is the third child's name? The answer is in the first two words: she is Tom's mother, so Tom is one of her children. The third child is Tom.

Brothers and sisters: count yourself

Ana has 3 brothers. Each of her brothers has 2 sisters. How many sisters does Ana have? The 2 sisters of each brother are the girls in the family, and Ana is one of them. So there is Ana and one more girl. Ana has 1 sister.

The hardest one says: each boy has as many brothers as sisters, and each girl has twice as many brothers as sisters. A boy does not count himself, so the boys must be one more than the girls. Now try small families and check the girls:

So there are 4 boys and 3 girls: 7 children. Check the boys too: each boy has 3 brothers and 3 sisters.

The bat and the ball

A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much is the ball? Almost everyone first thinks of 10 cents. Check it: if the ball is $0.10, the bat is $1.00 more, so $1.10. Then the total is $1.20, not $1.10. The fast answer fails the check.

Here is a method that always works. The bat is "the ball plus $1.00". So the total is two balls plus $1.00. Take the $1.00 away: $0.10 is left, and that is two balls. So the ball costs $0.05 and the bat costs $1.05. Check: $0.05 + $1.05 = $1.10.

1. Take the difference away from the total.
2. What is left is the price of two of the cheaper thing. Divide it by 2.
3. Add the difference back to get the more expensive thing, and check the total.

A brick and a half

A brick weighs 1 kg plus half a brick. How much does a whole brick weigh? Think of the brick in two halves. The sentence says one brick = 1 kg + half a brick. So the 1 kg must be the other half of the brick. If half a brick is 1 kg, the whole brick is 2 kg.

Prices work the same way. A book costs $10 plus half of its own price. The $10 is the other half of the price, so the book costs $20.