This document contains puzzles and mathematical tricks. It includes 5 puzzles titled "The Bus Number", "The Gong", "Problem from Lilavati", "Good Guess", and "At the Fete". It also includes 5 math tricks titled "Food as Wages", "Boxes within Boxes", "Same Speed, Same Time", "Four and Four Mice", and "Dearer Numbers". Each puzzle and trick is presented along with the question and answer to solve it using mathematical reasoning. The document aims to entertain the reader with interesting math problems and their step-by-step solutions.

1. ONLY GENIUS WILL
OPEN THIS!!!
Have some fun with mathematics

2. CONTENTS
PUZZLES TO PUZZLE YOU
FUN TRICKS

3. Puzzles To Puzzle You
1) The Bus Number
2) The Gong
3) Problem From Lilavati
4) Good Guess
5) At The Fete

4. The Bus Number
While visiting a small town in the Kashmir , I
lost my overcoat in a bus. When I reported the
matter to the bus company I was asked the
number of the bus. Though I did not remember
the exact number I did remember that the bus
number had a certain peculiarity about it. The
number plate showed the bus number was a
perfect square and also if the plate was turned
upside down, the number would still be a
perfect square – of course it was not?
I came to know from the bus company they
had only five hundred buses numbered from 1
to 500.
From this i was able to deduce the bus
number.

6. The answer is……
The bus number
By experiment we find that the only
numbers that can be turned upside down
and still read as a number are 0, 1, 6, 8 and
9.
The numbers, 0, 1 and 8 remain 0, 1
and 8 when turned over, but 6 becomes 9
and 9 becomes 6. Therefore, the possible
numbers on the bus were 9, 16, 81, 100,
169, or 196. However, the number 196 is
the only number which becomes a perfect
square when turned over because 961 is
the perfect square of 31.
Therefore, 196 is the correct answer.

7. The Gong
Supposing a clock takes 7
seconds to strike 7. how long will
the same clock take to strike 10?

9. The answer is……
The gong
While striking 7 the clock strikes its first
gong at 7 o’clock and it strikes 6 more at
regular intervals. These 6 intervals take 7
seconds so that the intervals between gongs
is 7/6 seconds. However, to strike 10 there
are 9 intervals each taking 7/6 seconds for a
total of 10 1/2 seconds.

10. Problem from Lilavati
Here is an ancient problem from
bhaskaracharya’s lilavati.
A beautiful maiden, with beaming eyes,
asks me which is the number that,
multiplied by 3, then increased by three-
fourths of the product, divided by 7,
diminished by one-third of the quotient,
multiplied by itself, diminished by 52, the
sqaure root found, addition of 8, division
by 10 gives the number 2?
Well, it sounds complicated, doesn’t it?
No, not if you know how to go about it.

12. The answer is……
Problem from Lilavati
28 is the answer.
The method of working out this
problem is to reverse the whole process-
multiplying 2 by 10, deducting 8, squaring
the result and so on.

13. Good guess
In order to win a free visit to the
dentist, students had to guess the exact
number of gumballs in a fish bowl. The
students guessed 45, 41, 55,50 and 43,
but no one won. The guesses were off by
3, 7, 5, 7 and 2 (in no given order). From
this information, determine the number
of gumballs in the bowl.

15. The answer is……
Good Guess
Forty-eight gumballs. Since two
guesses were off by seven and no
guesses were repeated, these values
had to refer to numbers at the
opposite extremes of the spread. The
two extremes are 41 and 55. If you
add 7 to one and take 7 away from the
other, you arrive at the middle
number of 48.

16. At the fete
A number of us went out together to a
charity fete one day. Our party consisted
of 4 different professional groups, namely
25 writers, 20 doctors, 18 dentists and 12
bank employees. We spent altogether
Rs.13,000.
Later it was found that 5 writers spent
as much as four doctors, that twelve
doctors spent as much as nine dentists,
and that six dentists spent as much as
eight bank employees.
How mush did each of the four
professional groups spend?

18. The answer is……
At the fete
The writers spent Rs.3500, the
doctors also spent Rs.3500, the dentists
spent Rs.4200 and the bank employees
spent Rs.2100. Thus, they spent
altogether Rs.13300. The five writers
spent as mush as four doctors, twelve
doctors spent as mush as nine dentists,
and six dentists as mush as eight bank
employees.

19. FUN TRICKS
1) Food as wages
2) Boxes within boxes
3) Same speed, same time
4) Four and four mice
5) Dearer numbers

20. Food as wages
Open person got a job in a hotel on
condition that he would get 80 rupees per day
as wages, but he would lose 100 rupees on
every day he was absent. The food would be
free. The account will be settled on
completion of 30 days.
Though the man started his work he was
absent for many days. After 36 days the
account was settled. What he got as wages
was only food. There was nothing to be given
or taken. If it was so, how many days did he go
for work in 36 days?

22. The answer is……
Food as wages
20 days

23. Boxes within boxes
There are six small boxes in a box.
In each small box there are again 6
small boxes.
Then what is the total number of
boxes?

25. The answer is……
Boxes within boxes
1 + [6 + (6 × 6)] = 43 boxes.

26. Same speed, same time
A plane takes 1 hour and 20
minutes to fly from A to B and only 80
minutes to return in the same speed.
What is the reason?

28. The answer is……
Same speed, same time
80 minutes and 1 hour and 20
minutes are one and the same thing.
This problem is meant to create
confusion in an inattentive reader.

29. Four and four mice
It took four minutes for four cats
to catch four mice. If each cat has
taken the same time to catch a mouse,
how much time will it take for a cat to
catch a mouse?

31. The answer is……
Four and four mice
Four minutes. The reason can be
explained. Four cats caught four mice.
This means one cat caught one mouse
only. To be more explicit, when one
cat of the four had caught one mouse
one, four minutes had passed.

32. Dearer numbers
153, 370, 371, 407
These four numbers were dearer
to the famous Indian mathematician
Sreenivasa Ramanujan. Why?

34. The answer is……
Dearer numbers
The importance of those four
numbers is given below:
153 = 13 + 53 + 33
370 = 33 + 73 + 03
371 = 33 + 73 + 13
407 = 43 + 0 3+ 73

35. THANK YOU
BY
TWINKLING STARS
P.ANUSHYA
S.KEERTHANA
S.ENIYA VIVITHA
N.SIVAKAMI
2nd B.Sc., Mathematics
N.M.S.S.V.N. COLLEGE