Question

Find out which total scores between 80 and 100 are impossible to achieve?

the competition consists of 25 multiple choice qs. pupils score 4 points for each correct answer but lose 1 point for each incorrect answer. if they don't answer a q they score 0 points on that q.

Answer 1

`99,98,97,94,93,89`

Explanation:

I'm not sure of a way to do this aside from working out each possibility. So let's see if maybe we can find one.

I think I'll use a chart to help with this:

`(("Right answers","No answer","Wrong answer","Score"),(25,0,0,100),(24,1,0,96),(24,0,1,95),(23,2,0,92),(23,1,1,91),(23,0,2,90),(22,3,0,88),(22,2,1,87),(22,1,2,86),(22,0,3,85),(21,3,0,84))`

I'll stop here and point out that we have a pattern - we can find a range of scores based on how far away the number of "right" is from 25:

`25xx4=100`
`24xx4=96-(0,1)=>96, 95`
`23xx4=92-(0,1,2)=>92,91,90`
`22xx4=88-(0,1,2,3)=>88,87,86,85`
`21xx4=84`

and at this point no other numbers will be skipped because the amount of subtraction from the 21 right will get us to 20 questions right.