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Question

A number is said to be rotated when its leftmost digit is

moved to the right end, and the other digits shift to the left.

3117 becomes 1173, 1731, 7311 and finally 3117 again,

on successive rotations.

It turns out that the Centigrade representations of certain

temperatures are the rotation of the Farenheit representations.

For example, if 413 degrees F were 134 degrees C - but it's not.

What is the lowest temperature for which this is true?

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1 - Assuming numbers below "absolute zero" are not relevant, and

2 - Assuming the temperatures are expressed as integers.

Lowest rotated Fahrenheit temperature to Celsius: -425F = -254C

(if the negative symbol is an issue, 40F = 04C; there is also 61F = 16C; 82F = 28C...)

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1 - Assuming numbers below "absolute zero" are not relevant, and

2 - Assuming the temperatures are expressed as integers.

Lowest rotated Fahrenheit temperature to Celsius: -425F = -254C

(if the negative symbol is an issue, 40F = 04C; there is also 61F = 16C; 82F = 28C...)

Great job Kid, :) , but looking for rotated integers for C.

Hint: every 9th F gets you integer C..

-425 -> -253.88...
40 -> 04.44... [clever with the 0...]
61 -> 16.11...
82 -> 27.77...[/code]

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Hello

This is my try

Well I dont think there is any such number. At least not till 100000F

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Well using excel, I did the following

Column A, start with 32 and each following cell +9

Column B, =(Cell A - 32) * 5/9)

Column C ==ALUE(RIGHT(Cell A,(LEN(Cell A)-1))&LEFT(Cell A)) This returns 32 as 23, or 41 as 14

Column D =IF(Cell C = Cell A, True, False)

Added a autofilter, and discovered that between 589,838 and -589,838 there is only one solution that is valid. (For the negatives, I compared absolute numbers)

527F = 275C

If not comparing absolute numbers, I think there is one more solution;

-40F = -40C, Moving the left most part of -40F and rotating returns 40F- which 40 = 40 All the way around.. However, this is a far fetched idea.

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What other number(s) fit the answer by going through the full rotation?

There is one other answer.

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The F/C temperature pairs that are integers make C multiples of 5.

Restricting F values not to have a leftmost digit of 0, we have

C=5+10N and F=41+18N.

Since C ends in 5, F must begin with 5.

For each power of 10, there is one possibility for a rotated match.

These are the ones I've found - either an exact match, or the closest to it.

59		 -> 15
527 -> 275 <- match
5297 -> 2925
52943 -> 29395
529403 -> 294095
5294111 -> 2941155 <- near miss
52941173 -> 29411745 <- near miss
529411757 -> 294117625
5294117651 -> 2941176455[/code]

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The F/C temperature pairs that are integers make C multiples of 5.

Restricting F values not to have a leftmost digit of 0, we have

C=5+10N and F=41+18N.

Since C ends in 5, F must begin with 5.

For each power of 10, there is one possibility for a rotated match.

These are the ones I've found - either an exact match, or the closest to it.

59		 -> 15

527		-> 275	  <- match

5297	   -> 2925

52943	  -> 29395

529403	 -> 294095

5294111	-> 2941155  <- near miss

52941173   -> 29411745 <- near miss

529411757  -> 294117625

5294117651 -> 2941176455

What about 35195F = 19535C or 35195 -> 51953 -> 19535 (We have a match on second rotation)

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Found two more:

44024F = 24440C

24440 => 44402 => 44024 (We Have a match)(This is doing in reverse order)

219551F = 121955C

121955 => 219551 (We have a match) (This is doing in reverse order)

Reverse order ie;

527 = 275 => 752 => 527 not like before where it was one rotation

Then my computer program crashed at 219551 so I will have to wait to continue up to 1,000,000,000,000,000

Edited by PolishNorbi

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Found two more:

44024F = 24440C

24440 => 44402 => 44024 (We Have a match)(This is doing in reverse order)

219551F = 121955C

121955 => 219551 (We have a match) (This is doing in reverse order)

Reverse order ie;

527 = 275 => 752 => 527 not like before where it was one rotation

Then my computer program crashed at 219551 so I will have to wait to continue up to 1,000,000,000,000,000

3666020 = 2036660 => 0366602 => 3666020 (Bingo!)

8547485 = 4748585 => 7485854 => 4858547 =>8585474 => 5854748 => 8547485 (Bingo!)

Computer Froze at 10,000,000 Again

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