Puzzles contest - 16 With Answers

[HELP]

1. Recently,
while in London, I decided to walk down the escalator of a tube
station. I did some quick calculation in my mind. I found that if I
walk down twenty-six steps, I require thirty seconds to reach the
bottom. However, if I am able to step down thirty-four stairs I would
only require eighteen seconds to get to the bottom.
If
the time is measured from the moment the top step begins to descend to
the time I step off the last step at the bottom, can you tell the
height of the stairway in steps?

2. We
all know that a chess board has 64 squares. This can be completely
covered by 32 cardboard rectangles, each cardboard covering just 2
squares.
Supposing
we remove 2 squares of the chess board at diagonally opposite comers,
can we cover the modified board with 31 rectangles? If it can be done,
how can we do it? And if it cannot be done, prove it impossible
.
3. A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice.How many cats do you think there were?Oh,
by the way let me clarify Just two points-it is not one cat killed the
lot, because I have said 'Cats' and it is not 999919 cats each killed
one mouse, because I have used the woni 'mice'.I can give you just one clue-each cat Ililled more mice than there were cats.


4. A friend of mine in Bangalore owns a horse-driven carriage.
It was found that the fore wheels of the carriage make four more
revolutions than the hind wheel in going % feet. However, it was also
found that if the circumference of the fore wheel was 3/2 as great and
of the hind wheel4f3 as great, then the fore wheel would make only 2
revolutions more than hind wheel in going the same distance of 96 feet.
Can you find the circumference of each wheel?

5. Here is a simple arithmetical puzzle set by Longfej\low in his own flowefY, poetical language.If
one-fifth of a hive of bees flew to the badamba flower, one-third flew
to the slandbara, three times the difference of these two numbers flew
to an arbour. And one bee continued to fly about, attracted on each
side by the fragr.ant Ketaki and Malati, what was the total number of
bees







Answers












1. If I walk 26 steps I require 30 seconds. If I walk 34 steps I
require only 18 seconds.
, Multiplying 30 by 34 and 26 by 18 we. get 1020 and 468.










The difference between 1020 and 468 is 552. When we divide this number
by the difference between 30 and 18, i.e.. by 12 we get the answer
46-the number of
steps in the stairway.
2. No
It cannot be done. Each rectangle covers one white square and one black
square, because on a chess board the
white and black
squares are always adjacent.


The two squares which we
remove from the chess board
are of the same
colour, and so the remaining board
has two more boxes of one colour than the other. And after the rectangles have covered 60 boxes,
there will be left two squares of the same colour.


Obviously the remaining
rectangle cannot cover these two squares.


3. Just one look at the number
999919 and we know that it cannot be a prime number. And if the problem has to
have only one answer, this number can have only two factors. The factors are
991 and 1009, both of which are primes.


We know that each
cat killed more mice
than there were cats,
and,therefore;the correct answer, clearly, is that 991 cats killed 1009 mice.


4. The forewheel is 8 feet in circumference and
the hind wheel 12 feet.
5. The
number of bees are 15










Edited by: HELP

[meenakshisekar]

. Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom.
If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom, can you tell the height of the stairway in steps?


ans:26stairs=30min
34stairs=18 min

hence((34*30)-(26*18))/30-12
ans:46

[meenakshisekar]

2.[/b] We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares.
Supposing we remove 2 squares of the chess board at diagonally opposite comers, can we cover the modified board with 31 rectangles? If it can be done, how can we do it? And if it cannot be done, prove it impossible

ans:
no it cannot be covered.b's when u remove 2 squares from the opposite diagonal one pair of the removed diagonal remains uncovered.

[meenakshisekar]

3.[/b] A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice.How many cats do you think there were?Oh, by the way let me clarify Just two points-it is not one cat killed the lot, because I have said 'Cats' and it is not 999919 cats each killed one mouse, because I have used the woni 'mice'.I can give you just one clue-each cat Ililled more mice than there were cats.

ans:
find out the factors of this no,991&1009
hence,cats=991,
mice=1009

[meenakshisekar]

. A friend of mine in Bangalore owns a horse-driven carriage. It was found that the fore wheels of the carriage make four more revolutions than the hind wheel in going % feet. However, it was also found that if the circumference of the fore wheel was 3/2 as great and of the hind wheel4f3 as great, then the fore wheel would make only 2 revolutions more than hind wheel in going the same distance of 96 feet.
Can you find the circumference of each wheel?


ans:
forewhel=8 feet
hind wheel=12feet

[meenakshisekar]

5.[/b] Here is a simple arithmetical puzzle set by Longfej\low in his own flowefY, poetical language.If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour. And one bee continued to fly about, attracted on each side by the fragr.ant Ketaki and Malati, what was the total number of bees


ans:let bees be x


((x/3+x/5)+3(x/3-x/5)+1)=x


ans is 15 bees.

[keerthi]

1. Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom.
If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom, can you tell the height of the stairway in steps?
Ans)46 steps

26 steps--------------30 seconds====case1
34 " --------------18 " " ====case2

this means tht (30-18=12)seconds MORE r required if not climbing(34-26=8)steps.

i.e. if not climbing 8 steps 12 sec r req extra to reach downstairs.
" " 1 " 12/8 =1.5 sec " "&nbsp ; " .
consider he doesn't climb any step at all ;means he lets the escalator take him down itself.

take case1:
we know if not climbing 1 step 1.5 sec xtra is req.so in not climbing 26 steps
26*1.5=39sec r req in EXTRA.so total time =39+30sec=69.this is the time of descent of escalator.
since 1 step time =1.5

no. of steps=69/1.5=46steps

ans:46

[keerthi]

2. We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares.
Supposing we remove 2 squares of the chess board at diagonally opposite comers, can we cover the modified board with 31 rectangles? If it can be done, how can we do it? And if it cannot be done, prove it impossible

Ans)Its not possible.
To cover the 2 squares with rectangles the 2 squares must be adjacent.
Bcoz if we remove 2 squares from diagonally opposite corners there will be two more non adjacent squares which cannot be covered.

[keerthi]

3. A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice.How many cats do you think there were?Oh, by the way let me clarify Just two points-it is not one cat killed the lot, because I have said 'Cats' and it is not 999919 cats each killed one mouse, because I have used the woni 'mice'.I can give you just one clue-each cat Ililled more mice than there were cats.

Ans)No of cats were 991

Clearly the No. of cats must be a multiple of 999919.
The only mutiple of 999919 are 1009 and 991.
As the no of cats are less than no of mice the no of cats = 991
no of mice = 1009

[keerthi]

5. Here is a simple arithmetical puzzle set by Longfej\low in his own flowefY, poetical language.If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour. And one bee continued to fly about, attracted on each side by the fragr.ant Ketaki and Malati, what was the total number of bees
Ans) 15 bees.


let the no of bees be 'x'


given (x/5+x/3)+3(x/3-x/5)+1=x


Solving we get x = 15