Puzzle 1
This puzzle is called 'Mamma's Age', and is taken from 'Amusements In Mathematics' by Henry Ernest Dudeney (1917).
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?
workings
hint
answer
print
Share Link — www.brainbashers.com/puzzle/zpyu
Hint
The answer isn't a whole number of years, and algebra might be required.
Answer
29 years 2 months.
Reasoning #1
This answer is taken directly from the original book.
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.
Reasoning #2
Here's my answer, with a little algebra.
If we call Tommy T, Mamma M and Papa P we can see that:
"our three ages add up to exactly seventy years" gives us:
(1) T + M + P = 70
"Just six times as old as you" gives us:
(2) P = 6 x T
In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:
(3) P + Y = 2 x (T + Y)
and "our three ages will add up to exactly twice as much as today" gives us:
(T + Y) + (M + Y) + (P + Y) = 140
which can be written as
(4) T + M + P + 3Y = 140
We can see from (4) and (1) that
3Y = 70
so
(5) Y = 70 ÷ 3
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
(6) T = 70 ÷ 12
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 2
What number is...
...three-quarters of eight-ninths of one-half of 2001?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share Link — www.brainbashers.com/puzzle/zrtd
Hint
Can the fractions be simplified?
Answer
667.
Reasoning
3 8 1
— of — of — of 2001
4 9 2
which simplifies to:
24
—— of 2001
72
which simplifies to:
1
— of 2001
3
Giving 667.
Puzzle 3
How many squares, of any size, can you find on this chessboard that do not contain a Rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share Link — www.brainbashers.com/puzzle/zrzl
Hint
How many 2x2 squares are there?
Answer
128.
Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are 6 squares of size 4 x 4.
There is 1 square of size 5 x 5.
A total of 62 + 41 + 18 + 6 + 1 = 128.
Puzzle 4
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 Copyright © Kevin Stone
workings
hint
answer
print
Share Link — www.brainbashers.com/puzzle/zdfx
Hint
How many tyre miles were travelled?
Answer
1,005 miles.
Reasoning
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.
next >