I have never been a math genius. Or even a math sub-genius. Or even a non-genius. In fact, I’m a bit of a Math Dunce. I need your help in solving a math problem.

Here’s what I need to figure out:
You have 30 words in each of three columns: A and B and C.

You can create sentences by choosing any word from column A and adding any word from B and any word from C.
Column A must follow column B must follow column C.

How many unique sentences can you create by picking one word from each column — all the words in all columns have been pre-vetted so there’s no chance of creating a sentence clinker — without repeating any sentences with identical words from each column?

When you have an answer, please post a comment and show your work to
help explain the logic of how you came to that conclusion!

Please also include any natural and unnatural laws you employed to help
you and any and all incantations invoked and magic spells you threw —
as well as the details of all the Voodoo that you do so well…

We’ll only pick a winner when a person not in your knowing
circle steps forward to confirm the answer is correct and then explains
the why of your math genius solution.

If you need more information in order to provide an answer, just
No name calling allowed. No taunting of the question allowed. No
mocking the simplicity of any obvious answers that are not obvious to

No comments extolling the virtues of your trained monkey who
solves math problems like this every day for bananas.

Then, for extra credit… if you used: AA+B+C… how many unique
sentences could you then create? And then what about AA+B+CC… and so
on… and so on… and so on… ?



  1. For ABC it is simply 30x30x30=27,000 sentences (Although I’d be intrigued to see the 90 words ;).
    To put it simply, you have 30 words to choose from in column A, each of those can be paired with 30 words from column B, each of those 30×30 AB combinations can then be paired with one of 30 words from column C, giving a result of 30^3.
    (I am assuming there are 90 words, and not 30 words repeated 3 times, in which case for sentences with non-recurring words the result would be 30x29x28=24,360)
    For a sentence such as AABC it would be 30x29x30x30=783,000 if you wanted non-repeating words from A and 30^4=810,000 if repeated instances were allowed.
    I’m sure you can deduce any other combinations of As, Bs and Cs from that …
    There are combinatory formulas for this if you’d like

  2. Mike!
    Thank you!
    I thought it was 27,000 but then I thought there’s NO WAY it could be that high a number and I had misunderstood something about something somewhere. πŸ˜€
    27,000 is unbelievable.
    Yes, all 90 words are unique!
    The rest of your math instruction about the double AA and such lost me… all those numbers… and the funny symbols… getting sleepy… hungry for… bananas…
    I can’t wait to see how you answer tomorrow’s question! :mrgreen:

  3. Gordon!
    Winners never sleep and they never use spreadsheets! πŸ˜€
    Here’s a new question for you: How long would it take to speak 27,000 three word sentences?

  4. Well now that’s an entirely different problem that is pretty much unsolvable thanks to variables such as word length and pronunciation of speaker. For example, if one of the words is caramel, some people would say it a little bit faster than others due to skipping the a.
    Never use spreadsheets, eh? Excel is my trained monkey. πŸ™‚

  5. Oh, and Gordon, go into your BolesUniversity.com email account, click on SETTINGS, and tell me if you have IMAP support listed along with Forwarding and POP.
    Janna has IMAP listed now! None of my accounts have it yet. Grrr!

  6. The expert (Mike) has already answered with what I would have managed to come up with and for the same reasons – that is about as far as my maths goes.

  7. P.S. —
    Anyone with a Gmail/Google Apps account should check their SETTINGS to see if they have IMAP on their account yet or not.
    Report back here what you find! πŸ˜€

  8. Hi Nicola!
    My math skills are so limited that I had the right answer and rejected it because it was too unbelievable. I STILL FIND IT UNBELIEVABLE! πŸ˜€
    I wonder how long it would take a barrel of monkeys to type 27,000 unique sentences?

  9. 189126.111465 seconds is 2 days, 4 hours, 32 minutes and 6.111168 seconds πŸ˜‰
    For info 3^4 simply means 3 to the power of 4 (3^2 would be 3 squared = 9) and the AA stuff was your extra credit, don’t I get a banana for that? πŸ˜‰

  10. Mike! You beat Gordon again!
    Ha! “Bwa-ha-harr!,” actually. πŸ˜†
    Wow! 2 days to speak all those sentences. Love that!
    You get no extra credit because I did not understand your answer and even explaining it a second time with that upward arching thingy didn’t help. Sorry! No credit because I’m stoopid! πŸ˜‰

  11. 27,000 is just the number of combinations. It’s still 3 words times 2.33etc seconds times 27,000 different combinations. πŸ™‚ Nobody needs to breathe in my math world. Hee hee.

  12. You’re too fast for me, spaceman! I have been up since 4:39 for various reasons and for a second there I thought I was wrong and wrote out how dumb I felt but then I remembered why I did it to begin with. πŸ™‚

  13. Gordon!
    We need to factor in breath. No rounding up or down.
    Each sentence starts with a breath that lasts 0.0023 seconds.
    The breath between A and B is 0.99832 seconds.
    The breath between B and C is 0.999887766 seconds.
    The breath between sentences is 1.28765 seconds.
    Dance, monkey, dance!

  14. How many monkeys in the barrel and what is their typing speed ?
    ( Hides under the desk)
    I am dreading tomorrows question as well now.

  15. P.S.
    Is it inherently unfair Janna has IMAP in her GApps account while Gordon and I do not? She cares not about IMAP while Gordon and I live and die by it.

  16. Nicola!
    There are 13 monkeys in the barrel. Five of them are missing three fingers. Six are wearing shoes. Two who have missing fingers and are wearing shoes are also wearing mittens. The bus driver’s name is Bob.
    Tomorrow’s question will be lots of fun!

  17. Based on your breathing, each sentence takes 10.292828561 seconds – no rounding. Seems like a lot of time for saying three words!
    Moving forward, taking that we get 277,906.371147 seconds which is 4631.77285245 minutes or 77.1962142075 hours or 3.2165089253125 days which is 0.00881235322003424 of a year!

  18. Excellent work, Gordon, and you didn’t let Mike beat you to the bananas this time! High marks!
    We speak slowly and do a lot of heavy breathing! πŸ˜€

  19. I hope you only included the space between sentences 26,999 times πŸ˜‰
    And the breath before is really part of the breath between … and that shouldn’t count for the first sentence either as you shouldn’t start the clock until you start speaking πŸ˜‰
    Or am I just fussy πŸ˜‰

  20. Mike!
    I wonder if your threw Gordon into the barrel wit your 26,999 intrigue?
    We should’ve added a “pause” factor of 2.009932 seconds between sentences to separate the sigh of successful completion and the breath of beginning again. πŸ˜€

  21. I honestly don’t see what the big to-do is about this imap thing. I mean, I feel overwhelmed as it is checking my gmail(s) from both the web and my phone – do I really need to bog down computer memory and hard drive space with my gmail(s)? πŸ™‚

  22. Gordon —
    The beauty of IMAP over pop or a web interface is that you can check your mail from multiple interfaces and see the same folders and mail messages. You don’t have to download anything. You can just peek to see what’s new. POP requires downloading. IMAP does not.

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