Saturday, September 7, 2013

Numbers of Syllables / Syllables of Numbers

When spoken aloud, the number 11 has three syllables, the number 105 has four syllables, and the number 1,200 has six syllables. Some puzzles on this general topic are below...feel free to put answers in the comments---or add more puzzles!  

1) Amy subtracted a three-syllable number from a three-syllable number and obtained a thirty-seven syllable number. What could her numbers have been?

2) What is the smallest number you can find with nineteen syllables?

(You should be able to do better than 13,012,321,012,001.)

3) What is the largest number you can find for which the number of syllables equals the sum of the digits?

4) What is the largest prime number you can find for which the number of syllables equals the sum of the digits?


radioactive_piano said...

Just to be That Person, are we limited to whole numbers? I'm looking at question 2 here and I'm getting all sorts of evil. ;-)

JasonZimba said...

I meant the puzzle to be limited to whole numbers - thanks for the clarifying question!

Cristian Ferreyra said...

My answer to number 2: 177,777
In Spanish: 127,422 (syllable trans: ci-en-to ve-in-te si-e-te mil, cua-tro-ci-en-to ve-in-te dos)

JasonZimba said...

Blowing my mind with the Spanish version! I wonder which language gives the smallest answer?

jeff said...

I blew #2. Cristian me beat by 594,000 :)

I feel pretty good about my other answers thanks to some downtime at work:
1) 12,000,000,000,000 - 23 = 11,999,999,999,977

3) 721,341,341,341,341,141 (48 syllables)
OR, now that i've figured out the nomenclature for numbers bigger than quadrillions thanks to the interwebs, 721,721,721,721,721,721,721,341,341,341,341,141
(721 decillion, 721 nonillion, 721 octillion, etc. = 108 syllables)

4) 102,701 (11 syllables)
i didn't look beyond the first 10,000 primes

By the way, does my inability to decipher the "Please prove you're not a robot" text mean that i'm a repliCAN'T?

JasonZimba said...

Yeah I have a hard time with captchas too...said the bot responding to Jeff's comment.

Don't know if people have seen but the link at the top of this post points to a book that gives standard nomenclature to decillions - sorry if that was obscure, I meant to save people from having to search around for that.

Love these answers, I'll aim to round them all up along with mine by Monday!

JasonZimba said...

A teacher friend is trying out these puzzles with her students - maybe we'll get some answers from them :-)

jeff said...

i see now that i made the same mistake on #3 as the 594,000-unit mistake on #2

plus i'm investigating alternate strategies for #3 cuz i doubt repetition is optimal

jeff said...

oh, and i can't wait to get beat down by a bunch of high school kids

JasonZimba said...

Well, they haven't gotten in touch yet, but I should point out, they're fifth-graders :-)

jeff said...

Here's my attempt at an upgraded #3
(999 decillion, 999 nonillion, 992 octillion, 111 heptillion, ... 111)

My childish "infinity+1" type answer is:
999,999,992,111,111,111,111,111,111,111,111,111-googolplexian 6
ie, {the above #} followed by {[a 6] preceded by [1 less than a googolplex of zeros]}