    Mathematical Puzzles  Puzzle 5 During the recent BrainBashers football competition, 5 schools were competing. Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost. Here are the final points after all of the matches: Longton     6 Fenton      5 Blurton     4 Hulton      2 Fulton      ==?== How many points did Fulton end the season with? [Puzzle Code = ZBIL] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZBIL Hint: How many games took place? Answer: 3. Since there were 5 teams in the league there were a total of 10 possible games (either way around):   Longton  vs  Fenton    Longton  vs  Blurton    Longton  vs  Hulton    Longton  vs  Fulton    Fenton   vs  Blurton    Fenton   vs  Hulton    Fenton   vs  Fulton    Blurton  vs  Hulton    Blurton  vs  Fulton    Hulton   vs  Fulton Since each game distributed 2 points to the two teams there were a total of 20 points available to the league. The results shown add to 17, leaving the remaining 3 to Fulton. Puzzle 6 If a bottle weighs eight ounces plus half a bottle... ...what is the weight of a bottle and a half? [Puzzle Code = ZPSD] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZPSD Hint: Find the weight of the bottle first. Answer: 24 ounces. The bottle weighs 16 ounces. As a bottle weighs eight ounces plus half a bottle we can write this as:    B = 8 + ½B Take ½ from both sides to get:    ½B = 8 So B = 16, which means B + ½B = 24. Puzzle 7 Can you find a number... ...whose double exceeds its quarter by 7. [Puzzle Code = ZHRW] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZHRW Hint: The number is less than 100. Answer: 4. 4's double is 8 and 4's quarter is 1.If the missing number is N, then:   2N = N + 7        -        4 Multiply throughout by 4:   8N = N + 28 Subtract N from both sides:   7N = 28 Divide throughout by 7:    N = 4 Puzzle 8 At a recent visit to the reptile house at the local zoo, I counted a total of 27 heads and 70 feet. I was counting snakes, lizards and people and I know that there were exactly twice as many lizards as people. How many snakes did I count? [Puzzle Code = ZLHO] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZLHO Hint: Snakes don't have legs. Answer: 6 snakes: 7 people and 14 lizards. If we have S snakes, L lizards and P people.The 27 heads gives us:    S + L + P = 27           The 70 feet gives us:      4L + 2P = 70           We also know that:            L = 2P           Using  in  gives:  4 x 2P + 2P = 70 So:          10P = 70            P = 7 Using P = 7 in  gives:      4L + 14 = 70           4L = 56            L = 14 Using L = 14 and P = 7 in  gives:   S + 14 + 7 = 27            S = 6 So S = 6, P = 7 and L = 14.     