Two Riddles
I am just wondering:
What is the largest integer consisting of distinct digits such that, in its English pronunciation, all the words start with the same letter?
I continue to wonder:
Share:What is the largest integer consisting of the same digit such that, in its English pronunciation, all the words start with distinct letters?
Murt:
Seems like 111/one hundred eleven would be the answer to the second
27 October 2011, 10:56 amMurt:
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 / seventysix, unless my lunch break has got me all confused.
27 October 2011, 11:14 amAnonymous Rex:
3012 and 111?
27 October 2011, 11:26 amBlaine:
For the first, how about this?
27 October 2011, 11:27 am3,012 = Threethousand twelve
Murt:
Oops. 3012 / three thousand twelve would be better for the first question.
27 October 2011, 11:29 amBlaine:
Drat! Anonymous Rex and I were typing at the same time and he beat me to it. ๐
27 October 2011, 11:30 amMurt:
Ha…Anonymous Rex beat me to catching my mistake.
27 October 2011, 11:30 amBlaine:
Okay, here’s an alternate answer.
“Two to the twentieth” = 1,048,576
27 October 2011, 11:36 amJoseph:
I’d go for 3029 on the first one. “Twentynine” is one word. ๐
27 October 2011, 11:43 amBlaine:
Okay Joseph, using your logic we could do better than that with “Thirtynine Thousand Twentyeight” = 39,028
27 October 2011, 11:47 ampruwyben:
In that case, why not go for Thirtynine thousand twentyeight?
27 October 2011, 11:58 amBob:
10^23
Ten To The Twenty Third
(People commonly omit the word “power”)
๐
27 October 2011, 12:03 pmObsessiveMathsFreak:
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.
27 October 2011, 12:24 pmaww:
In American English, it is not technically correct to say “and”, though many people do. I believe British English differs in this respect.
27 October 2011, 1:25 pmBrenda:
Thirteen thousand twenty = 13020
27 October 2011, 2:11 pmBrenda:
No, that repeats a zero.
27 October 2011, 2:12 pmSara:
99 followed by 300 zeroes…ninetynine novemnonagintillion
Although you could also add two nines every 30 digits or so (nonillion, novemdecillion, etc)
27 October 2011, 4:23 pmObsessiveMathsFreak:
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”
27 October 2011, 6:41 pmnate:
What about “a thousand one hundred eleven?”
27 October 2011, 7:54 pmAnonymous 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?)
28 October 2011, 10:06 amTanya 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
28 October 2011, 10:17 amRyan:
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.
29 October 2011, 3:28 amAlex:
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 nonnegative numbers, in which case the answer is 0. Or were you looking for positive integers?
17 November 2011, 6:41 pmMolly:
Thereโs no answer unless we restrict ourselves to nonnegative 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)
9 November 2012, 12:59 pmMolly:
(I also got “3012” and “111” for the two riddles at the top)
9 November 2012, 1:01 pmAhaan 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 nonscientific 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! ๐
12 November 2012, 9:25 pmTanya Khovanova:
Ahaan,
All digits must be distinct.
12 November 2012, 9:57 pm