## What’s in the Name?

• 4, 6, X, 9, 10, 12, 14, 15, 16
• 1, 2, 6, 24, 120, X, 5040, 40320, 362880
• 2, X, 3, 4, 7
• 1, 2, 3, 4, 5, 6, X, 8, 9, 153, 370, 371
• X, 2, 3, 4, 5, 6, 7
• 6, 28, 496, 8128, X, 8589869056, 137438691328
• 0, 1, 1, X, 4, 7, 13, 24, 44, 81

This is the puzzle I designed for yesterday’s event at the Museum of Mathematics. This puzzle is without instructions — figuring out what needs to be done is part of the fun. Solvers are allowed to use the Internet and any available tools. The answer to this puzzle is a word.

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### 7 Comments

1. #### Oscar Cunningham:

Nice puzzle. The steps lead very logically from one to the next. I still can’t remember the sequence ending 153, 370, 371, but I’m sure it will come back to me eventually.

2. #### Puzzling:

Oscar:
1³+5³+3³=153, 3³+7³+0³=370, etc.

3. #### Puzzling:

I give up. It just seems like a bunch of numbers. 🙂

4. #### Oscar Cunningham:

@Puzzling I thought it might be something of the form ‘numbers which are the sum of {some function} of their digits’. In particular I noticed that having both 370 and 371 would be consistent if the function had f(0) = 0 and f(1) = 1. But then seeing all the single digit numbers threw me off, because surely for them to satisfy the property the function would have to be the identity. I’ve now looked at the OEIS to find the true answer for that sequence.

5. #### Taposik:

Wow! NUMBERS…that’s all they are. I don’t know what to do with them. I am not from maths. But I have learned a lot of things from this puzzle. Who could have thought that numbers could be narcissistic too? So thanks.

6. #### Puzzling:

@Oscar, here are some hints: 1) Order the sequences by the which term is missing. 2) Figure out the *name* of each sequence. The number of terms given is a clue. 3) How does the missing term relate to each sequence’s name? 4) Put it all together and you’ll figure out the word that is missing.

7. #### Tanya Khovanova's Math Blog » Blog Archive » What’s in the Name? Solution:

[…] recently posted my puzzle designed for the MoMath […]