1) Fill the 3 gallon pitcher and pour it into the 5 gallon pitcher. Now fill the 3 gallon pitcher again and fill the 5 gallon pitcher to capacity. What remains in the 3 gallon pitcher is one gallon of juice.
2) 10x10=100÷1/2=200+12=212 *NOTE: For another way to look at this - I noticed that the corresponding answer to puzzle 1 says "10x10=100÷1/2=200+12=212", when in fact it should be "8x10=80÷1/2=160+12=172" as you have 8 fingers and 2 thumbs!
3) 9
4) If there is to be only one winner, than there are 99 loses, therefore there were 99 matches. You can also do this with math: in round 1 there would be 50 matches to produce 50 winners, round 2 would have 25 matches to produce 25 winners, round 3 would have 12 matches to produce 12 winners ( one person of the 25 winners would have to wait until later to play again ), round 4 would have 6 matches to produce 6 winners, round 5 would have 3 matches to produce 3 winners, round 6 would have 2 matches ( the player left out before would now play to make it an even field ) to produce 2 winners, these 2 would play for the championship. So: 50+25+12+6+3+2+1=99