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If 31x + 30y + 29z =366 , find x+y+z ? (x,y,z are natural numbers)

+2 votes
posted May 13, 2015 by Ankit Kamboj

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3 Solutions

+2 votes
Best answer

Very tricky

366 days in a year -

31*7+30*4+29*1= 366

So x+y+z = 12 i.e. number of months in a year

solution May 13, 2015 by Salil Agrawal
There are two answers:  first set:  1, 4, 7
                                        second set:  2, 2, 8
The above answers were arived at visually by using a simple matrix consisting of 3 columns (x,y,z) and 10 rows (29x1, 29x2 etc, then 30x1, etc, then 31x1 etc. and going up to 10 for each multiplication).  And just by looking at the numbers it should only take a few attempts to get the 2 sets of number.
+1 vote

Considering the number 29,30,31 as number of days of month and number of days in leap year - 366 .
= 29*1+ 30*4+31*7
= 366

solution Jun 20, 2016 by anonymous
+1 vote

Simple solution for 2 different answers using a matrix:

enter image description here

solution Sep 13, 2016 by George Davros

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