# Question 37

Challenge question #37 (14/11/2016)

Junior Question

November 2016
S
M
T
W
T
F
S
$1$
$2$
$3$
$4$
$5$
$6$
$7$
$8$
$9$
$10$
$11$
$12$
$13$
$14$
$15$
$16$
$17$
$18$
$19$
$20$
$21$
$22$
$23$
$24$
$25$
$26$
$27$
$28$
$29$
$30$
Notice that the four numbers
$13$
$14$
$20$
$21$
have the property that
$\ 14\times20-13\times21$
$=$
$\ 280-273$
$=$
$\ 7$
Prove that any four numbers
$a$
$b$
$c$
$d$
in the calendar will have the property $bc-ad=7$.
Hint

Senior Question

Consider a set of $6$ points in the plane which have been joined by $10$ distinct line segments. Show that at least one triangle is formed.
Hint