A simple number puzzle

[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.

[Leif]

Spoiler

x = 1
y = 4
z = 7

[HansV]

@Leif: correct!

[AlanMiller]

I'm sure this came up some months ago.

Alan

[HansV]

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

[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

[Leif]

I'm sure this came up some months ago.

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...

[AlanMiller]

Leif is again correct.

Alan

[HansV]

Ah, OK

[AlanMiller]

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.

Alan

[John Gray]

I'd forgotten about your batch file prowess. I'll have to analyze it and see how it ticks.

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!

[HansV]

Code: (...)

That is very clever, John. It would have taken me months to come up with that. Nice to have a second solution...