    Mathematical Puzzles  Puzzle 5 Three teachers were discussing how long they had been teaching. Alex and Blake had been teaching for a total of 36 years. Charlie and Blake had been teaching for a total of 22 years. Charlie and Alex had been teaching for a total of 28 years. How long had each been teaching? [Puzzle Code = ZKLD] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZKLD Hint: Alex had been teaching 6 years longer than Blake. Answer: Alex had been teaching 21 years. Blake had been teaching 15 years. Charlie had been teaching 7 years. Alex and Blake had been teaching for a total of 36 years. Charlie and Blake had been teaching for a total of 22 years. Charlie and Alex had been teaching for a total of 28 years. Let Alex = A, Blake = B and Charlie = C, then:    A + B = 36           C + B = 22           C + A = 28        If we use  -  we have:    A - B = 6         If we use  +  we have:    2A = 42     A = 21 By  B = 15. By  C = 7. Puzzle 6 Tommy: "How old are you, Mamma?" Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years." Tommy: "That's a lot, isn't it? And how old are you, Papa?" Papa: "Just six times as old as you, my son." Tommy: "Shall I ever be half as old as you, Papa?" Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day." Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..." Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache." Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma? [Puzzle Code = ZPYU] Mamma's Age. Amusements In Mathematics by Henry Ernest Dudeney (1917).    Direct Link: www.brainbashers.com?ZPYU Hint: The answer involves years and months. Answer: The age of Mamma must have been 29 years 2 months. That of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father. The answer above is taken from the original book, here is another version of the answer:If we call Tommy T, Mamma M and Papa P we can see that: "our three ages add up to exactly seventy years" leads to    T + M + P = 70 (1) "Just six times as old as you" leads to    P = 6 x T (2) In an unknown number of years (Y) "Shall I ever be half as old as you" leads to:    P + Y = 2 x (T + Y) (3) and "our three ages will add up to exactly twice as much as to-day" leads to:    (T + Y) + (M + Y) + (P + Y) = 140 which can be written as    T + M + P + 3Y = 140 (4) We can see from (4) and (1) that    3Y = 70 so    Y = 70 ÷ 3   (5) Using (2) and (5) in (3) we have                  P + Y = 2 x (T + Y)    6 x T + 70÷3 = 2 x (T + 70÷3)           4 x T = 70÷3               T = 70÷12 (6) We can now use (6) in (2) to see that:    P = 6 x T    P = 6 x 70÷12    P = 70÷2 And using the values for T and P in (1) we have:                          T + M + P = 70     70÷12 + M + 70÷2 = 70 Multiply throughout by 12 to give:    70 + 12 x M + 420 = 840               12 x M = 840 - 420 - 70               12 x M = 350                    M = 350÷12 So: Tommy = 70÷12   = 5.83333  = 5 years 10 months.     Papa  = 70÷2    = 35       = 35 years.     Mamma = 350÷12  = 29.1666  = 29 years 2 months. Puzzle 7 What number is... ...three quarters of eight ninths of one half of 2001? [Puzzle Code = ZRTD] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZRTD Hint: Can the fractions be simplified? Answer: 667.3   8   1   24   1 - x - x - = -- = - 4   9   2   72   3 And 1/3 x 2001 = 667. Puzzle 8 I recently travelled from my home town to a distant music concert, on a pedal tricycle of all things! My wonderful, three wheeled tricycle. I knew that the epic 2,345 mile trip would wreak havoc on the tyres, but luckily I took along 4 spares! Instead of waiting for any single tyre to fail, I decided that I would rotate the tyres evenly, making sure that by the end of the trip all seven tyres had travelled exactly the same distance. What was the distance that each tyre travelled? [Puzzle Code = ZDFX] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZDFX Hint: How many tyre miles were travelled? Answer: 1,005 miles. A total of 2,345 miles were travelled and at any one time, three tyres were on the tricycle. Therefore 3 x 2,345 = 7,035 tyre miles were travelled, which was shared equally by the 7 tyres. And 7,035 ÷7 = 1,005.     