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Topic: Upside Down LCD display (Read 5971 times) |
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waka
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Hi!
Worked on this problem for a while, then got annoyed and brute-forced the answer.
So now I am stuck with the solution and no process.
Not really sure how to calculate this, although it seems that you count 7 numbers as "flippable" for every 10 digits, 70 for each 100, 700 for each 1000, etc. So, the millionth digit would be 7^6th flippable combination, but this doesn't tell me how to actually find the millionth flippable combo. Doh!
waka
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klbarrus
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Re: Upside Down LCD display
« Reply #1 on: Jul 27th, 2002, 11:57pm » |
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Hey waka, what answer did you get?
Was is 11555511 by any chance?
If so, I might have a method and can explain it. But right now I'm not sure it is correct and need to double check some stuff.
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NickH
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Re: Upside Down LCD display
« Reply #2 on: Jul 28th, 2002, 7:56am » |
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We are essentially counting in base 7, using LCD digits 0, 1, 2, 5, 6, 8, 9. The question is asking for the base 7 representation of the decimal number 1000000.
This can be found by repeated (decimal) division of 1000000 by 7, reading the remainders in reverse order. We get 11333311. Then convert to LCD digits to get 11555511.
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Nick's Mathematical Puzzles
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klbarrus
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Re: Upside Down LCD display
« Reply #3 on: Jul 28th, 2002, 11:28am » |
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Yes, that is my method. The only digits that can be reversed are 1,2,5,6,8,9,0; so there are 7 number for each 10, 49 for each 100, 343 for each 100, etc.
So convert to base 7, and then translate the result to LCD representation.
E.g. 15th flippable number: 15 base 10 = 21 base 7, 2nd LCD digit is 2, 1st LDC digit is 1 -> 21. 17th flippable number: 17 base 10 = 23 base 7, 2nd LCD digit is 2, 3rd LCD digit is 5 -> 25. 1000000 is 11333311 in base 7, 1st LCD digit is 1, 3rd LCD digit is 5 -> 11555511
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Eric Yeh
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Re: Upside Down LCD display
« Reply #4 on: Aug 2nd, 2002, 10:05am » |
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I agree with this answer for the problem as stated; however, I think I've also seen the problem stated in such a way where flipping "10" should not be valid. ("01" isn't a particularly valid number, after all!) If anyone's interested, this is a variant that throws a twist into the simpler base 7 soln.
Best,
Eric
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continuum
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Re: Upside Down LCD display
« Reply #5 on: Aug 29th, 2002, 7:15pm » |
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My method and answer were the same too... But I had to use the information that 21 is the 15th flippable number, what I disagree. I think 0 should be considered the first flippable number, rather than 1. After all, 0<1 and 0 can be displayed in an LCD.
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titan
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Re: Upside Down LCD display
« Reply #6 on: Oct 11th, 2013, 7:59am » |
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I wanted to understand that why has this been said:
"We are essentially counting in base 7, using LCD digits 0, 1, 2, 5, 6, 8, 9. "?
And why has base 7 come into picture at all?
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Grimbal
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Re: Upside Down LCD display
« Reply #7 on: Oct 11th, 2013, 9:26am » |
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Because we are dropping all number that contain 3, 4 or 7.
It is like counting with only the remaining 7 digits.
So it is like counting in base 7 where the digits are represented by 0,1,2,5,6,8,9.
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titan
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Re: Upside Down LCD display
« Reply #8 on: Oct 11th, 2013, 9:33am » |
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Woohoo! got it, most of what you said.
But why are we dropping 3,4 and 7?
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Grimbal
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Re: Upside Down LCD display
« Reply #9 on: Oct 11th, 2013, 9:50am » |
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Because these numbers cannot be reversed. We are not dropping 3,4 and 7, we are dropping the whole number that contains any of these digits.
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| « Last Edit: Oct 11th, 2013, 9:50am by Grimbal » |
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titan
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Re: Upside Down LCD display
« Reply #10 on: Oct 11th, 2013, 11:48am » |
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Sorry, but this is what I don't understand again. Why can't such numbers be reversed? What is meant by being able to reverse? Give example.
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towr
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Re: Upside Down LCD display
« Reply #11 on: Oct 11th, 2013, 12:16pm » |
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on Oct 11th, 2013, 11:48am, yoyoy wrote:| Sorry, but this is what I don't understand again. Why can't such numbers be reversed? What is meant by being able to reverse? Give example. |
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By reverse is meant upside down.
a 1 upside down is still a 1, the same for 2,5,8 and 0. A 6 upside down is 9 and vice versa.
But a 3 upside down is E, 4 upside down is h and 7 upside down is L, none of which are digits, and so don't form a valid number (except if you allow numbers in 'scientific notations' like 21E12 = 21 * 10 12)
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Wikipedia, Google, Mathworld, Integer sequence DB
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titan
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Re: Upside Down LCD display
« Reply #12 on: Oct 11th, 2013, 12:36pm » |
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Yes.yes.yes!
I was about to post that I have got it!!
Why did they say that reverse of 1995 is 5661? (It is its base 7 representation though)
It should be 1662. No?
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Grimbal
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Re: Upside Down LCD display
« Reply #13 on: Oct 11th, 2013, 12:47pm » |
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Type 1995 on a pocket calculator and return it upside down.
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