According to a's guess,

Total score a

=66× 10%+89×40%+86×20%+68×30%

=6.6+35.6+ 17.2+20.4

=79.8

(2)

The scores of A, B and C on the puzzle are all the same, and so are the recovery scores of the Rubik's Cube.

Therefore, the sum of the converted scores of each puzzle and Rubik's cube of A, B and C is 20 points.

Therefore, the sum of the conversion scores of skillfully solving interesting problems and mathematical application is 167-20×2= 127.

That is 60 x%+80 y%+80 x%+90 y% = 127.

Multiply both sides by 10 to get: 6x+8y+8x+9y= 1270.

That is14x+17y =1270.

One set of solutions is: x=30, y=50.

According to this conversion rate,

The total score of A = 20+89× 30%+86× 50% = 20+26.7+43 = 89.7.

The total score of B = 20+60× 30%+80× 50% = 20+18+40 = 78.

The total score of C =20+80×30%+90×50%=20+24+45=89.

So a and c can win the first prize.