A simple number puzzle

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HansV
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A simple number puzzle

Post by HansV »

From today's The Guardian:
Find a solution to the equation

28x + 30y + 31z = 365

where x, y, and z are positive whole numbers.
Solutions in spoiler tags, please.
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Hans

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Leif
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Re: A simple number puzzle

Post by Leif »

Spoiler
x = 1
y = 4
z = 7
Leif.

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HansV
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Re: A simple number puzzle

Post by HansV »

@Leif: correct! :wine:
Regards,
Hans

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AlanMiller
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Re: A simple number puzzle

Post by AlanMiller »

I'm sure this came up some months ago. :confused:

Alan

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HansV
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Re: A simple number puzzle

Post by HansV »

Not here in the Puzzles forum during the last year-and-a-half (I didn't check further back).
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Hans

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John Gray
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Re: A simple number puzzle

Post by John Gray »

Code:
Spoiler

Code: Select all

@echo off
setlocal enabledelayedexpansion
for /l %%x in (1,1,13) do (
  for /l %%y in (1,1,13) do (
    for /l %%z in (1,1,12) do (
      set /a prod=28*%%x
      set /a prod+=30*%%y
      set /a prod+=31*%%z
      if !prod!==365 echo X is %%x, Y is %%y, Z is %%z
    )
  )
)
endlocal
pause 
Solutions:
Spoiler
X is 1, Y is 4, Z is 7
X is 2, Y is 1, Z is 9
John Gray

“The only difference between reality and fiction is that fiction needs to be credible.” - Mark Twain.

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Leif
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Re: A simple number puzzle

Post by Leif »

AlanMiller wrote:I'm sure this came up some months ago. :confused:
HansV wrote:Not here in the Puzzles forum during the last year-and-a-half (I didn't check further back).
Spoiler
I suspect Alan is obliquely referring to what the numbers (can) relate to...
Leif.

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AlanMiller
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Re: A simple number puzzle

Post by AlanMiller »

Leif is again correct. :evilgrin:

Alan

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HansV
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Re: A simple number puzzle

Post by HansV »

Ah, OK :blush:
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Hans

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AlanMiller
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Re: A simple number puzzle

Post by AlanMiller »

John Gray wrote:Code:
Spoiler

Code: Select all

@echo off
setlocal enabledelayedexpansion
for /l %%x in (1,1,13) do (
  for /l %%y in (1,1,13) do (
    for /l %%z in (1,1,12) do (
      set /a prod=28*%%x
      set /a prod+=30*%%y
      set /a prod+=31*%%z
      if !prod!==365 echo X is %%x, Y is %%y, Z is %%z
    )
  )
)
endlocal
pause 
Solutions:
Spoiler
X is 1, Y is 4, Z is 7
X is 2, Y is 1, Z is 9
I'd forgotten about your batch file prowess. I'll have to analyze it and see how it ticks. :bravo:

Alan

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John Gray
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Re: A simple number puzzle

Post by John Gray »

AlanMiller wrote:I'd forgotten about your batch file prowess. I'll have to analyze it and see how it ticks. :bravo:
It's not particularly difficult and entirely 'brute force', without any refinements. The upper bounds of the FOR loops assume that the values of the other two variables were zeros. It could almost have been ported from Fortran!
John Gray

“The only difference between reality and fiction is that fiction needs to be credible.” - Mark Twain.

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HansV
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Re: A simple number puzzle

Post by HansV »

John Gray wrote:Code: (...)
That is very clever, John. It would have taken me months to come up with that. Nice to have a second solution... :thumbup:
Regards,
Hans