In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?
+44 I presume the boxes and inequalities look like such
[ ] < [ ] > [ ] < [ ] > [ ]
We can set the inequality as
a < b > c < d > e
To solve the question, there are 2 cases:
case 1:
b=4 d=5 (or the other way around)
Then we can set a, c, and e, as any number (1, 2 or 3)
so for case 1 we have 2*3!=2*6=12
case 2:
b=5, a=4 (or on the other side, d=5, e=4)
In this case we know that d has to be 3, other wise the inequality won't *work*
we have two ways to put 1, and 2 into the equation, so
For case 2, there are 2*2=4 ways
Add them together: 4+12=16
(wow this sounded a lot simpler in my head) Please confirm this
