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Which one does not belong?

Logic and puzzles · level 1, lesson 3 of 6

A question to start

Here are four shapes. Which one does not belong?

A B C D

Maybe you said B, because it is the only blue one. Your friend might say C, because it is the only small one. Who is right?

Here is the surprise: you can both be right. In fact, in this puzzle there is a good answer for every one of the four shapes. Can you find a reason for A, B, C and D? (A is the hardest. Look very closely at it.)

The idea

The odd one out

In a "which one does not belong" puzzle, you look at a few things and try to find one that is different from all the others in some way. People also call it "the odd one out".

The answer is not just a letter. The answer is a letter and a reason. "C, because it is the only small one" is an answer. "C" on its own is only half an answer.

A good reason picks out exactly one

What makes a reason good? Two checks.

  1. The reason must be true for the one you picked.
  2. The reason must be false for every one of the others.

Let us check "B, because it is blue".

  • Is B blue? Yes. ✓
  • Is A blue? No. Is C blue? No. Is D blue? No. ✓

B passes both checks, so it is a good answer.

Now let us check a bad one: "D, because it is big".

  • Is D big? Yes. ✓
  • Is A big? Yes! ✗

Stop. A is big too, so "big" does not pick out D alone. That reason fails. When you find a reason, always look at all the others and make sure none of them has it too.

Every shape can be the odd one out

Here are reasons for all four shapes from the start.

Shape Reason Others have it?
A It is the only one with a dot in the middle. B: no dot. C: no dot. D: no dot. ✓
B It is the only blue one. A, C, D are all orange. ✓
C It is the only small one. A, B, D are all big. ✓
D It is the only square (the only one with corners). A, B, C are all circles. ✓

Notice how the puzzle was made. Each shape is different from the others in its own way. So there is no single "right answer". There are four good answers, and the fun is finding them all.

Many ways of being different

When you look for the odd one out, ask yourself lots of questions. Each question is like a sorting rule from the first lesson.

  • Colour: is one a different colour?
  • Size: is one bigger or smaller?
  • Shape: is one a different shape? Does one have corners?
  • Number: does one have more or fewer of something (legs, sides, dots)?
  • What it does: can one fly, roll, swim, or make a noise?
  • Where it lives or comes from: is one from the sea, or the farm, or the sky?

Here is the link to sorting. When you find a reason, you have really sorted the four things with a rule, and found that the rule makes a group of one on its own, and a group of three together.

blue not blue B A C D

Some reasons are more interesting than others

"2, because it is the smallest number" is a true reason. It picks out exactly one. So it is a good answer! But it works for almost any puzzle with numbers, so it does not tell us much. A reason like "7, because it is the only one you cannot share into pairs" is more interesting, because it tells you something special about 7.

All reasons that pass the two checks are correct. The more interesting ones are more fun.

Worked examples

Example 1. Animals. Which one does not belong: cat, dog, cow, hen?

Let us try some reasons and check each one.

  1. "Hen, because it has 2 legs." Hen: 2 legs ✓. Cat, dog, cow: 4 legs each ✓. Good.
  2. "Hen, because it lays eggs." Hen ✓. The others do not lay eggs ✓. Good. (Two reasons for the same answer!)
  3. "Cow, because it is the biggest." Cow ✓. Cat, dog and hen are smaller ✓. Good.
  4. "Cat, because it has fur." Cat ✓. But the dog has fur too ✗. Not good. The cow has fur as well.
  5. "Cat, because it can climb trees." Cat ✓. Dogs, cows and hens do not climb trees ✓. Good.

What about the dog? "Dog, because it barks." Dog ✓. Cats meow, cows moo, hens cluck ✓. Good. So every animal can be the odd one out, if you find the right reason.

Example 2. Numbers. Which one does not belong: 2, 4, 7, 8?

2 4 7 8
  1. "7, because you cannot put 7 dots into pairs." Make pairs: 2 is one pair, 4 is two pairs, 8 is four pairs, but 7 is three pairs and one left over. ✓ This is the most interesting reason.
  2. "2, because it is the smallest." True, and no other is smaller. ✓
  3. "8, because it is the biggest." ✓
  4. "4, because it is a number on a dice." Check the others: 2 is on a dice too! ✗ Not good.

Look at the dot picture. The 7 has a dot all alone with no partner. Pictures can help you see a reason.

Example 3. Is it a good reason? Ella looked at a car, a bike, a bus and a boat. She said: "The boat, because it has no wheels." Check:

  • Boat: no wheels ✓.
  • Car: wheels. Bike: wheels. Bus: wheels. ✓

Good reason. Her brother said: "The bike, because you ride it outside." Check: you ride a car, a bus and a boat outside too. ✗ Not a good reason. A better one: "The bike, because it has no engine," or "because it has only 2 wheels."

Example 4. Make your own. Can you make a set of four where every one has its own reason? Here is one way: start with three things that are the same, then change one thing about each.

  • Start: big green triangle, big green triangle, big green triangle.
  • Make the second one orange. Make the third one small. Add a fourth that is a big green square.
  • Now the first triangle is the only one that is "plain". Give it something extra: a dot, or a thick border.

Now each shape has one special thing. That is exactly how the puzzle at the start was made.

Try it

  1. Which one does not belong: apple, banana, carrot, pear? Give a reason, and check it.
  2. Which one does not belong: 5, 10, 13, 15? Give a reason.
  3. Ben says, about a duck, a swan, a robin and a goose: "The robin, because it has feathers." Is that a good reason?
  4. In the shapes from the start, give a second reason for D.
  5. Which one does not belong: sun, moon, star, cloud? Find two different answers.
  6. Which one does not belong: 3, 6, 9, 11? Can you find a reason for 3?
  7. Make your own "which one does not belong" with four things, and ask someone at home to find all the answers.
Answers
  1. Carrot, because it is a vegetable (the others are fruits). Check: apple, banana and pear are all fruits. ✓ Another: "banana, because it is the only one you peel before eating" (most people eat the skin of an apple and a pear). Another: "banana, because it is long and curved".
  2. 13, because you do not say it when you count by fives (5, 10, 15, 20, ...). Check: 5, 10, 15 are all in the count by fives. ✓ Another: "5, because it has only one digit." Another: "10, because it is the only one you can share into pairs."
  3. No. All four birds have feathers, so "has feathers" does not pick out the robin. A good reason: "The robin, because it does not swim" or "because it is the smallest".
  4. "D, because it has 4 corners" or "D, because it has straight sides". Check: A, B and C are circles, with no corners and no straight sides. ✓
  5. "Cloud, because it is not out in space" (the sun, the moon and the stars are all far away in space; clouds float in our own air). "Moon, because it goes round the Earth" (the sun, the stars and the clouds do not). Another: "Cloud, because it is made of water drops." Any reason that passes the two checks is fine.
  6. 11, because you do not say it when counting by threes (3, 6, 9, 12). For 3: "3, because it is the only one that is smaller than 5." Or "6, because it is the only one you can share into pairs."
  7. Any set is fine. Ask your helper to say each reason out loud and check it against the other three.

Common mistake

Forgetting to check the others. "The cat, because it has fur" sounds right, until you notice that the dog has fur too. A reason only counts if none of the other things has it.

Thinking there is only one right answer. In these puzzles there are often several right answers. If your answer is different from your friend's, do not just say "you are wrong". Ask "what is your reason?" and check it together. You might both be right.

Where it leads