Venn diagram approach to Contest question #16

There are 71 students in the Travel Club. They discovered that 37
members have visited Canada, 34 have visited Mexico, 33 have been
to Scotland, 13 have visited Canada and Mexico, 11 have been only
to Scotland, and 15 have been only to Canada. 9 have been to
Canada and Mexico, but not to Scotland. Some club members have
not been to any of the three foreign countries, and some have been
to all three countries.

How many students havenít been to any of the three countries?







Here is an alternative way to solve this problem, using matrices.

a+b+c+d=37,c+d+f+g=34,e+b+c+f=33,c+d=13,e=11,a=15,d=9,a+b+c+d+e+f+g+h=71

AX = B		X = A-1B

B =	37
	34
	33
	13
	11
	15
	9
	71
	
	 		 1 	 1	 1	 1	 0	 0	 0	 0		   
	0	0	1	1	0	1	1	0
	0	1	1	0	1	1	0	0
A =	0	0	1	1	0	0	0	0
	0	0	0	0	1	0	0	0
	1	0	0	0	0	0	0	0
	0	0	0	1	0	0	0	0
	1	1	1	1	1	1	1	1
	

	0	0	0	0	0	1	0	0
	1	0	0	-1	0	-1	0	0
	0	0	0	1	0	0	-1	0
	0	0	0	0	0	0	1	0
A-1 =   0	0	0	0	1	0	0	0
	-1	0	1	0	-1	1	1	0
	1	1	-1	-1	1	-1	-1	0
	-1	-1	0	1	-1	0	0	1

https://matrix.reshish.com/inverCalculation.php

	15
	9
	4
 X =	9
	11
	9
	12
	2

2 people have visited no countries