1. Draw the Timetable of the Meetings in Slide 11

Solution 21

1. Draw the timetable of the meetings in slide 11.

One of the solutions:

Andy(A), Benjamin(B), Chris(C), Dorothy(D), Ewan(E), Francisca(F), Greg(G), Hillary(H)

Day1 / AB / CD / EF / GH
Day2 / AC / BH / DE / FG
Day3 / AD / BG / CF / EH
Day4 / AE / BF / CG / DH
Day5 / AF / BE / CH / DG
Day6 / AG / BD / CE / FH
Day7 / AH / BC / DF / EG

2. Finish the table on slide 24

Sun / Mon / Tue / Wed / Thu / Fri / Sat
1,a1,a2 / 1,b1,b2 / 1,c1,c2 / 1,d1,d2 / 1,e1,e2 / 1,f1,f2 / 1,g1,g2
b1, d1, f1 / a1, d2, e2 / a1, d1, e1 / a2, b , c / a2, b1, c1 / a1, b2, c1 / a1, b1, c2
b2, e1, g1 / a2, f2 , g2 / a2, f1, g1 / a1, f , g / a1, f1 , g2 / a2, d2, e1 / a2, d1, e2
c1, d2, g2 / c1, d1, g1 / b1, d2, f2 / b1, e , g / b2, d1, f2 / b1, e2, g1 / b2, d2, f1
c2, e2, f2 / c2, e1, f1 / b2, e2, g2 / c1, e , f / c2, d2, g1 / c2, d1, g2 / c1, e1, f2

¢Extra Credit: Explain why the last algorithm fails when n is not a prime number

Assume n is a composite number. (n=a*b, a<b<n where a and b are natural numbers.)

Consider the last column of Day1 and Day (a+1),

Day1 / Day(a+1)
n / n
2n / 2n-a
. / .
. / .
. / .
(b+1)n / [(b+1)n-a*b]=[(b+1)n-n]= (b+1)n
. / .
n^2 / [n^2-a(n-1)]

*** [x]= x+kn such that x+kn is one of the possible number on that row.

By contradiction, n must be a prime number.