Puzzles contest - 21 With Answers

[HELP]

1 . I
have a box. The two dimensions of the box are 4" and 3". Compute the
third dimension of the box so that the space diagonal of the box is an
integer.

2 . Mammu
and I, we were on a tOllf of West Germany. It was a very cold winter
evening. We stepped in the street to walk to a coffee shop. Mamrnu is
only five and a half years old. We were dressed similarly. Who do you
think felt colder?

3. What is the special about this number


4. In
India water lillies grow extremely rapidly in the ponds. If the growth
enlarged so much that each day it covered a surface double that which
it filled the day before, so that at the end of the 20th day if
entirely covered the pond, in which it grew, how long would it take two
water lillies Qf the same size at the outset and at the same rate of
growth to cover the same pond?

5. Here is a piece of Mnemonic: Now I - even I, would cele~rate In rhymes unapt the great Immortal syracusan rivaled never more, who in his wondrous lore Passed OJ; before, Left men his guidance How to circles mensurate. Can you tell what it signifies? 62 And if h is the height of the room, then h2 + (24J5)2 = 562 and h = 16. Thus the height of the room is 16 ft. Total time required







Answers
















1. 12 inches. The diagonal of
the end is 5. Therefore the space diagonal will be the hypotenuse of a right angle,
one of whose legs is 5, the other an integer. Three numbers, known as the
Pythagorean Triples, can be represented by: ml
Yz (m2 -1) and Yz(m2
+ 1) because fT12 + (Yz(m2 - 1))2 =
(Yz (m2 + 1))2 52 + 122 = 132. The other
dimension is 12. inches.Therefore the space diagonal
is 13 inches.




2. Here again there is an
example of a problem that does not seem mathematical at all at the first glance but a closer
look will reveal that this is a problem that cannot be solved without geometry.
We all know that things usually cool down from the surface. So, a child
standing out in the street, in the cold, feels the cold more than a similarly
dressed adult, though the amoimt of heat in each cubic centimetre of the body
is almost the same in the case of both. A child has a greater cooling surface
per one cubic centimetre of the body than an adult. . This also explains why a person's fingers
and nose suffer more from cold and get frost bitten oftener than any other
parts. of the body whose surface is not so great when compared to their
volume. .


This same theory explains why
splint wood catches fire faster than the log from which it has been chopped
off. Heat spreads from the surface to the whole volume of a body and therefore
the heat sets splint wood on fire faster than the log.




3. This is the only known
number that is a sum of two cubes in two different ways. Example: 103 + 93 = 1729, 123 + 13 = 1729 This is popularly known as Ramanujam's number. There
is an interesting story about it. The story goes this way. When Ramanujam was
sick in the hospital,




Prof. Hardy, his tutor paid
him a visit. Prof. Hardy told Ramanujam that he rode a taxicab to the hospital,
with a very unlucky number. When Ramanujam e"nqll1red what the number was, Prof. Hardy replied: 1729.
Ramanujam's face lit up with a smile and he said that it was not an unlucky
number at aU, but a very interesting number, the only number that can be
represented as the sum of two cubes in two different ways!


4. 19 days.


5. Pi to 30 decimal places.









Edited by: HELP

[keerthi]

4. In India water lillies grow extremely rapidly in the ponds. If the growth enlarged so much that each day it covered a surface double that which it filled the day before, so that at the end of the 20th day if entirely covered the pond, in which it grew, how long would it take two water lillies Qf the same size at the outset and at the same rate of growth to cover the same pond?


Ans)19 days.


with one flower the pond would be half full by 19 days


so with 2 flowers the pond will be filled completly in 19 days

[keerthi]

2 . Mammu and I, we were on a tOllf of West Germany. It was a very cold winter evening. We stepped in the street to walk to a coffee shop. Mamrnu is only five and a half years old. We were dressed similarly. Who do you think felt colder?
Ans) Mammu feels colder
The general principle says Smaller objects get cooled at faster rate then bigger ones.

[keerthi]

1 . I have a box. The two dimensions of the box are 4" and 3". Compute the third dimension of the box so that the space diagonal of the box is an integer.
Ans) 12
the diagonal of that face(4,3) is 5
Since the space diagonal is hypotenuse of traingle whose one of the legs is 5,the least possible value of other leg is 12 to make the hypotenuse an integer.

[ankit.k.saxena]

1)the face dioagonal is 5 and the space diaganal is 13 so the third dimension is 12.


2)the bigger the surface area the greater the heat loss thus i'll feel much colder


3) no. not given


4)the pond will get filled up in 19 days with 2 lillies.


5)the data is not clearly posted