perplexus.info :: Logic : Look b4 U leap

Home > Logic

Look b4 U leap (Posted on 2020-10-02)

Find a solution to the equation:
29x + 30y + 31z = 366

Rem: x,y,z must be positive

See The Solution Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Explanation to Puzzle Answer: Method 3

| Comment 7 of 8 |

29x+30y+31z=366

=> 31(x+y+z) + z-x = 366

=> x+y+z - (2x+y)/31 = 12 - 6/31

So, x+y+z=12

and, 2x+y=6

If x>=3, then from the second equation, we have:

y<=0.

This is a contradiction.

x =2 gives y=2, so that: z=12-4=8

x=1 gives y=4, so that: z=12-5= 7

Then, (x, y, z) = (2, 2, 8) and, (1, 4, 7) are the only possible solutions.

Posted by K Sengupta on 2022-06-14 23:44:19

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (15)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info