## Two Riddles

1. #### Murt:

Seems like 111/one hundred eleven would be the answer to the second

2. #### Murt:

Basically, you’re very quickly tripped up with the first question by not being able to say “hundred,” so the answer has to be a two digit number. I guess it’s probably 76 / seventy-six, unless my lunch break has got me all confused.

3. #### Anonymous Rex:

3012 and 111?

4. #### Blaine:

3,012 = Three-thousand twelve

5. #### Murt:

Oops. 3012 / three thousand twelve would be better for the first question.

6. #### Blaine:

Drat! Anonymous Rex and I were typing at the same time and he beat me to it. 🙂

7. #### Murt:

Ha…Anonymous Rex beat me to catching my mistake.

8. #### Blaine:

“Two to the twentieth” = 1,048,576

9. #### Joseph:

I’d go for 3029 on the first one. “Twenty-nine” is one word. 🙂

10. #### Blaine:

Okay Joseph, using your logic we could do better than that with “Thirty-nine Thousand Twenty-eight” = 39,028

11. #### pruwyben:

In that case, why not go for Thirty-nine thousand twenty-eight?

12. #### Bob:

10^23

Ten To The Twenty Third

(People commonly omit the word “power”)

😛

13. #### ObsessiveMathsFreak:

3012: I think you have to say three thousand _and_ twelve.

At first I thought of 76, but then I thought of “seventy six score” = 76*20=1520, but then I thought of “sixty six squared” = 66^2=4356, but _then_ I thought of “three times three times two times two to the two times three times three” = 3*3*2*2^(2*3*3) = 4718592. Then I really thought about it and I said, OK.

I want to find the largest possible 2^x * 3^y with 10 or less distinct digits, so I want 2^x *3^y < 10^10 or x*log(2) +y*log(3) < 10*log(10). Now the upper bounds on x and y individually are floor(10*log(10)/log(2))=33 and floor(10*log(10)/log(3))=20, so it shouldn’t take too long to check all these combinations. So I (cheated) used the computer to check the 376 valid combinations.

Of these, the largest number appears to be:

“two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two times two ” or 2^29 = 536870912

Of course, I have unquestionably cheated (twice!) here by using the vagaries of the english language, and a computer.

14. #### aww:

In American English, it is not technically correct to say “and”, though many people do. I believe British English differs in this respect.

15. #### Brenda:

Thirteen thousand twenty = 13020

16. #### Brenda:

No, that repeats a zero.

17. #### Sara:

99 followed by 300 zeroes…ninety-nine novemnonagintillion

Although you could also add two nines every 30 digits or so (nonillion, novemdecillion, etc)

18. #### ObsessiveMathsFreak:

It took me a while, but I think I got the second riddle.

“The biggest repeating numeral integer having an english pronunciation with completely distinct first letters”

19. #### nate:

What about “a thousand one hundred eleven?”

20. #### Anonymous Rex:

Wow, this post got a lot of comments!

Here’s a fun puzzle: what’s the largest number that in its (American) English spelling has distinct letters?

(This is a variation, of sorts, on the standard puzzle: what’s the *only* number whose letters are in alphabetical order?)

21. #### Tanya Khovanova:

Rex,

I know that. The only number whose letters are in alphabetical order is FORTY. I do have my Number Gossip: https://www.numbergossip.com/40

22. #### Ryan:

Great riddles!

Here is one that I recently solved.

What is the smallest number divisible by the first three prime numbers and the first three composite numbers? Explain.

23. #### Alex:

Great riddles!

Here is one that I recently solved.

What is the smallest number divisible by the first three prime numbers and the first three composite numbers? Explain.

There’s no answer unless we restrict ourselves to non-negative numbers, in which case the answer is 0. Or were you looking for positive integers?

24. #### Molly:

There’s no answer unless we restrict ourselves to non-negative numbers, in which case the answer is 0. Or were you looking for positive integers?
|
|
|
|
Well, if Ryan did want positive integers like Alex said, then I believe the answer is 120….

(I know this is like a year late, lol)

25. #### Molly:

(I also got “3012” and “111” for the two riddles at the top)

26. #### Ahaan Rungta:

For Question #2, 111 definitely sounds like the best answer. For Question #1, there seem to be many interpretations. Bob’s logic with 10^23 seems to be so clever that it’s almost cheating! If that isn’t allowed in this riddle and only “saying aloud the non-scientific representation” is allowed, then “Ten Trillion, three thousand thirty three (10,000,000,003,033)” sounds like the best I can think of at the moment. Awesome problems – thank you! 🙂

27. #### Tanya Khovanova:

Ahaan,

All digits must be distinct.