Question

Question 2. We saw in class that any amount of n cents, for na 12 , can be paid as a sum of 4- cent and 5-cent stamps. Let fin) be the number of ways n cents can be written as the sum n=4x+5y for x,y nonnegative integers; fin) can be zero. (a) Tabulate (n.f(n)) for n=0,1,...,100.

Answer 1

100

Explanation naux+ry 0 If n=o .n=4(0) +500) is one way only @ af n=1 » 1= 4x+ sy is not possible for I any non-regative integer X and y so o way 3 If n=4> 4=461)+560) a one way only ☺ gf n= 6 6= not possible to way O gf na aa a= 4(1) +5(1) Tone way only 0 If n=20 20=4(5) +500) lag ways =410) +500)

1 If n = 40 3 ways 40= 4(10) +560) = 4(5)+504) = 40)+518)) Note: 0 for 12 shEdo If his divisible by u then I ways otherwise I way . h for aos nauo it nis divisible by u then I ways - otherwise I way ② for no sncoo 1. itn is divisible by 4 then 3 ways otherwise I way only ☺ for bo snago if an is divisible by 4 then Yways otherwisto e soa na 100 - if n is divisible by 4 then 5 ways otherwise o

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