Using 5 cent 11 cent and 17 cent stamps what are all possibl

Using 5 cent, 11 cent, and 17 cent stamps, what are all possible amounts of postage that can not be formed? Prove your answer. Part of your answer needs to use strong induction.

Solution

Upto 10 only 5 and 10 can be formed and rest cannot be formed

From 11 to 16

All except 11,15,16 cannot be formed

Beyond 11 all number of the form: 5k+1 can be formed eg. 16=11+5 and so on

Beyond 17 all numbers of teh form:5k+2 can be formed. eg. 22=17+5

11*2 =22 which is also 5k+2 number

So all number of the form: 5k+3,5k+4 from 11 to 32 cannot be formed

11*3=33

So for all numbers larger tahn 33 all numbers of the form:5k+3 can be formed eg. 38=33+5 and so on

34=2*17

So for all numbers larger than 34 all numbers of the form 5k+4 can be formed

Hence beyond: 34 all numbers can be formed.