Math Puzzles
Question 1: A beggar takes what he can get. A beggar on the street can make one cigarette out
of every 6 cigarette bud that he finds. After one whole day of searching, the beggar finds a total
of 72 cigarette buds. How many cigarettes can he make and smoke from the buds he found?
Answer:
He can make 14cigarettes. If the beggar can make a whole cigarette from 6 butts then he can
make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12
butts, from which he can make another 2 cigarettes.
Question 2: How can we get a total of 120 by using five zeros 0,0,0,0,0 and any one
mathematical operator.
Answer:
The factorial of Zero is 1
(0!+0!+0!+0!+0!)!
=(1+1+1+1+1)!
=5!
= 5*4*3*2*1
=120
Question 3: At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?
Answer:
There were 12 people in the party.
With (n+1) people, the number of handshakes is the sum of the first n consecutive numbers:
= 1+2+3+ ... + n.
= n(n+1)/2
Therefore the equation becomes
n*(n+1)/2 = 66
n*(n+1) =132
Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Considering that 66 is a relatively small number, we can also solve this problem with a hand
calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that is entered is n
which in this case is 11.
Question 4: There are n sweets in a bag. Six of the sweets are Red. The rest of the sweets are
yellow.
Jon takes a sweet from the bag and eats it. Jon then takes at random another sweet from the
bag. He eats the sweet. The probability that Jon eats two Red sweets is 1/3. Show that n²-n90=0
Answer:
The answer is n = 10.
10² - 10 - 90 = 0
If Jon has 10 sweets he has a 6/10 chance of pulling out anred sweet first time and then a 5/9
chance of pulling one out second time.
Equation becomes
= (6/10) X (5/9)
= 30/90
= 1/3