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#1 2016-11-13 03:32:08
- evene
- Member
- Registered: 2015-10-18
- Posts: 272
MMC 2015 Problem Help!
(1) Catherine and Doris enter the first floor of the skyscraper, Taipei 101, and have to get to a meeting on a certain floor. The elevator is at the very top floor. It takes the elevator 1 minute to reach the first floor from the top floor, and 1 second to move up each floor. Alternatively, if you decide to walk up the stairs, while Catherine waits for the elevator and then takes the elevator up. They both arrive at the meeting at the same time. On which floor was the meeting held?
(2) Let x be a two-digit positive integer. Let y be the two digit integer that results from switching the order of the digits of x. Let z=x+y. How many possibilities are there for x such that z is a perfect square?
(3) The natural numbers 1,2,3,4,...,999 are written down in one long string. The string looks like this: 12345...998999. How many 1s appear in this string.
(1) seems similar to a classic speed distance problem, but I'm not too sure how to set up the equation.
I just don't know where to start on (3)
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#2 2016-11-13 04:57:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: MMC 2015 Problem Help!
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2016-11-13 05:28:46
- evene
- Member
- Registered: 2015-10-18
- Posts: 272
Re: MMC 2015 Problem Help!
By the way, I got a 15 day trial of Mathematica. How do I use it? What are the commands?
I can't simply enter something like Solve[something here!] for a. Mathematica doesn't understand that...
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#4 2016-11-13 05:34:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: MMC 2015 Problem Help!
That is what you do essentially with solve.
For instance for your problem 3
champ[n_] := ToExpression[StringJoin[Table[ToString[i], {i, n}]]];
Count[IntegerDigits[champ[999]], 1]Want easier than that?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2016-11-13 05:53:12
- evene
- Member
- Registered: 2015-10-18
- Posts: 272
Re: MMC 2015 Problem Help!
Yes.
How do you remember all of the commands? I have no idea what "ToExpression", "ToString i" and all those random i/n means.
As much as I can guess, you're telling Mathematica to find the number of digits with 1 from 1 to 999....
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#6 2016-11-13 05:57:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: MMC 2015 Problem Help!
Hi;
How do you remember all of the commands?
M has more than 5000 commands. You can not remember them all, at least I can not. But the commands are sometimes self explanatory and the Help, very good. Read the Help pages or hit F1 on any command you type. Also, you can ask for help on forums.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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