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Subject: Friday math puzzle (lite) rss

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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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There are 10 kinds of people who understand binary: Those who do, and those who don't.
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More taste!
Less filling!
Less probability and advanced math required!

The new Riddler ExpressTM offered up its inaugural puzzle today.

I might actually have a shot at answering this one!!

Count Von Count, the counting count on “Sesame Street,” counts aloud on Twitter.
If he counts up by one with each tweet — “One!” “Two!” “Three!” … “Five hundred thirty eight!” etc. — how high can he go before hitting the 140-character limit?
Note: The count is enthusiastic, and must end all of his tweets with an exclamation point.


Riddler Express
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Josh Jennings
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Spoiler (click to reveal)

It seems like the first time he reaches 140 characters would be:
1,103,373,373,373
One Trillion One Hundred Three Billion Three Hundred Seventy Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

I first guess for the first time he goes over would be (142 characters):
1,113,323,373,373
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

That would make the highest he could go be one less than that (140 characters):
1,113,323,373,372
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Two!

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Erik Henry
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thermogimp wrote:
Spoiler (click to reveal)

It seems like the first time he reaches 140 characters would be:
1,103,373,373,373
One Trillion One Hundred Three Billion Three Hundred Seventy Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

I first guess for the first time he goes over would be (142 characters):
1,113,323,373,373
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

That would make the highest he could go be one less than that (140 characters):
1,113,323,373,372
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Two!


Spoiler (click to reveal)
Assuming of course that Twitter doesn't change their character limit at some point over the next 35,000 years. (Assuming one text per second.)

At least vampires live forever, so it's not like it's an unrealistic scenario...
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Michael Berg
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I think you're too high, but that's because I used "and" when counting (which doesn't fit the example).


Spoiler (click to reveal)
one hundred and one billion three hundred and seventy three million three hundred and seventy three thousand three hundred and seventy three!

aka 101,373,373,373!

That's 141 characters, so he'd stop at 101,373,373,372! #AhAhAh
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Erik Henry
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From what I understand, using "and" is preferred in British English but not in "American" English. Not that it isn't still quite common.
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Josh Jennings
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thermogimp wrote:
Spoiler (click to reveal)

It seems like the first time he reaches 140 characters would be:
1,103,373,373,373
One Trillion One Hundred Three Billion Three Hundred Seventy Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

I first guess for the first time he goes over would be (142 characters):
1,113,323,373,373
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!

That would make the highest he could go be one less than that (140 characters):
1,113,323,373,372
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Two!



Spoiler (click to reveal)
Oops, I think I'm off by 50,000.

I wrote a program to help me out a little bit and it helped me to realize that I missed:

1,113,323,323,373
One Trillion One Hundred Thirteen Billion Three Hundred Twenty Three Million Three Hundred Twenty Three Thousand Three Hundred Seventy Three!

This is 141 characters and 50,000 lower than my previous number. So now I think the solution is:

1,113,323,323,372


edit:

Spoiler (click to reveal)
Arg, and this is wrong too. I've found a solution that's roughly 50 million lower: 1,113,273,373,373 (141 chars). Dang. I think I need to go about this differently.
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Erik Henry
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thermogimp wrote:
Dang. I think I need to go about this differently.

Maybe start from the other end until you find one that's 140 characters or less? whistle



(Sorry, it's Friday afternoon)
 
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Josh Jennings
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Erik17 wrote:
thermogimp wrote:
Dang. I think I need to go about this differently.

Maybe start from the other end until you find one that's 140 characters or less? :whistle:



(Sorry, it's Friday afternoon)


Hah! Well, the problem is that the length of the string changes variably and if you were actually to count through 1 trillion+ numbers it takes an incredibly long time, even with computrs.

I think that I found the actual solution now, and here's how I did it:

Spoiler (click to reveal)
First, I noted that within each group of 3 digits, the longest strings are all the same. For example, Three Hundred Seventy Three is the longest in the hundreds group as well as in the thousands group, the millions group, and so on. I decided to create a list of the top 10 highest character counts for each number between 1 and 999. I used my program to help me do this and this was the result:

Longest String[0]: 373, Written: Three Hundred Seventy Three, Chars: 27
Longest String[1]: 323, Written: Three Hundred Twenty Three, Chars: 26
Longest String[2]: 173, Written: One Hundred Seventy Three, Chars: 25
Longest String[3]: 123, Written: One Hundred Twenty Three, Chars: 24
Longest String[4]: 121, Written: One Hundred Twenty One, Chars: 22
Longest String[5]: 117, Written: One Hundred Seventeen, Chars: 21
Longest String[6]: 113, Written: One Hundred Thirteen, Chars: 20
Longest String[7]: 111, Written: One Hundred Eleven, Chars: 18
Longest String[8]: 103, Written: One Hundred Three, Chars: 17
Longest String[9]: 101, Written: One Hundred One, Chars: 15

Cool! Now, I just need to count up adding the group name each time as well as spaces and the exclamation point. So that's what I did:

373! = 27 + 1(!) = 28
1,373! = 3(one) + 1(space) + 8(thousand) + 1(space) + 27 + 1(!) = 41
373,373! = 27 + 1(space) + 8(thousand) + 1(space) + 27 + 1(!) = 65
1,373,373! = 3(one) + 1(space) + 7(million) + 1(space) + 65 = 77
373,373,373! = 27 + 1(space) + 7(million) + 1(space) + 65 = 101
1,373,373,373! = 3(one) + 1(space) + 7(billion) + 1(space) + 101 = 113
373,373,373,373! = 27 + 1(space) + 7(billion) + 1(space) + 101 = 137
1,373,373,373,373! = 3(one) + 1(space) + 8(trillion) + 1(space) + 137 = 150

So now we know that we've gone over and that the number needs to be at least 1 trillion. The largest number of characters for anything less is only 137. Now the task is to reduce this number a low as possible while still being above 140. Since lowering the higher number groups first results in a bigger drop, that's what I tried. I looked at the list above and realized that 111 (One Hundred Eleven) is exactly 9 characters less than 373 and so would drop us right to the required 141 characters. Anything lower will drop us below 141 characters and we can't make those characters up in the lower value groupings.

I used my program to double check this number and it told me that the written equivalent is indeed 141 characters:

Number: 1111373373373, Written: One Trillion One Hundred Eleven Billion Three Hundred Seventy Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Three!, Chars: 141


This means that our answer must be:

1,111,373,373,372!
One Trillion One Hundred Eleven Billion Three Hundred Seventy Three Million Three Hundred Seventy Three Thousand Three Hundred Seventy Two! (139 characters).
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Robert Wesley
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shake We're naught "falling" for A-N-Y "'bananas'" in 'camels' "tailpipes"! surprisecaravan
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Andy Andersen
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I'm really getting tired of being asked to think on Fridays.
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Erik Henry
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Josh got it right!

http://fivethirtyeight.com/features/how-big-a-table-can-the-...
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