A mom was stumped by her first grader’s homework and posted the problem online to ask for help, as reported by Today.com via Yahoo News.

Which word is the odd one out?

friend
desk
toothbrush
egg
silver

Explain why.

As usual, watch the video for a solution.

Which Word Is The Odd One Out?

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“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

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Answer To Which Word Is The Odd One Out?

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

The list is a bit challenging for these types of questions, as no particular word would stand out to me.

friend
desk
toothbrush
egg
silver

After some thought I reasoned the answer would be silver because the color silver is an adjective and every other choice is a noun. This was the intended answer, and it was reported the class had just learned about nouns.

But I did a poll on YouTube and over 55,000 people voted and provided different justifications for all of the other answers too!

Nearly 50% felt that friend was the odd one out. Friend is a relationship and a concept, whereas all of the other items can be physical objects that do not change. But you might have a friend one day who is not a friend the next day.

The next popular choice was silver at around 23%. You could also say that silver is an uncountable noun whereas the others are all countable nouns.

The next choice was toothbrush at around 15%. This stands out as the longest of the words. It also lacks the letter E which is present in all of the other words. Toothbrush is also unique as a compound word consisting of the words tooth and brush.

The next choice was egg at around 11%. One justification is to count the letters in each word. Friend has 6, desk has 4, toothbrush has 10, egg has 3, and silver has 6. Every other word has an even number of letters while egg has an odd number of letters. So egg is literally the odd one out!

Only 3% of people voted for desk. So it would seem that desk is not really an odd one out. However, that itself makes it odd! Every other choice has an obvious reason for standing out, but desk is odd since it has no obvious reason!

There is also an interesting mathematical justification. Triangular numbers are numbers represented as the sum of integers from 1 to n, as those numbers can precisely be arranged in a triangular grid. The triangular number 10 can be represented like this:

1
1 1
1 1 1
1 1 1 1
…

The first triangular number is 1, then it is 1 + 2 = 3, then it is 1 + 2 + 3 = 6, and the next is 1 + 2 + 3 + 4 = 10.

So let’s go back to the number of letters in each word. Friend has 6, desk has 4, toothbrush has 10, egg has 3, and silver has 6. Every word besides desk has a triangular number of letters, whereas desk at 4 letters is not a triangular number of letters (of course 4 is a square number, not triangular number).

So desk can be the odd one out.

In summary, there are justifications for each of the answer choices, and it is the reasoning that is most important.

References

Today.com via Yahoo news
https://news.yahoo.com/mom-stumped-1st-graders-homework-023732843.html

LLM picture
https://commons.wikimedia.org/wiki/File:Multiple_attention_heads.png
DancingPhilosopher, CC BY-SA 4.0 via Wikimedia Commons

Poll
https://www.youtube.com/post/UgkxnpXa_kaR1A8_MliOTY-ZqdhY1klr4WYT

Triangular number
https://en.wikipedia.org/wiki/Triangular_number

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