Various Puzzles
Your Piggy Bank
Dad gives you money every day to put in your new piggy bank. He gives money to you in such a way that the money in the piggy bank doubles with each passing day.
If Dad gives you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your piggy bank gets full on the 16th day.
(a) On which day will your piggy bank be half-full?
For example, type 6 if your answer is 6th day.
(b) In addition to Dad's contributions, if Mom also gave you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then on which day would your piggy bank be half-full?
For example, type 6 if your answer is 6th day.
Black or Brown Gloves
Mr. Brown has 12 black gloves and 10 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?
Bicycles or Tricycles ?
Last weekend, I went to play in the nearby park. It was real fun! I rode my new bicycle that Mom had gifted me on my birthday.
On reaching the park, I saw that there were a total of 15 bicycles and tricycles. If the total number of wheels was 38 , how many tricycles were there?
Monkeys and Bananas
Suppose 6 monkeys take 6 minutes to eat 6 bananas.
(a) How many minutes would it take 4 monkeys to eat 4 bananas?
(b) How many monkeys would it take to eat 30 bananas in 30 minutes?
The Carpenter and the Nails
A 27" x 27" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 28 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?
The Shadow
A pillar 8 feet tall casts a shadow 4 feet long on the ground. If the pillar was 10 feet tall, how many feet in length would the shadow be ?
Chalk it Out
Your teacher has a total of 16 chalks. When a chalk reduces to 1/4 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day, how many days would the 16 chalks last?
The Snail on the Wall
A snail creeps 6 ft up a wall during the daytime. After all the labor it does throughout the day, it stops to rest a while... but falls asleep!! The next morning it wakes up and discovers that it has slipped down 2 ft while sleeping.
If this happens every day, how many days will the snail take to reach the top of a wall 58 ft in height?
Painting Job
A painting job can be completed by 8 painters in 21 days. If 16 more painters join the team 6 days after starting work on the job, then how many more days are required to complete the job?
Quiz Marks
Teacher: You appeared for 6 quizzes, and your average marks in them were 85.
Student: How did I fare in English?
Teacher: Well, your average in English Language and English Literature is 85.
Student: So, how was my performance in the remaining subjects?
Teacher: I am sure you can figure that out for yourself.
Can you help the student find his average marks in the remaining subjects?
Add Quickly
Can you find a quick and elegant way to add the numbers from 1 to 44 ?
In other words, what is the sum you obtain in the following case:
1 + 2 + 3 + ....... + 44 =
First Day at School
It was Stacy's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."
If there were 13 children in the class, how many total handshakes were there?
Game of Chocolates
Last vacation, my cousin came over to stay at my home. We made the most of her stay at my place... and I even earned a few chocolates.
Everyday, we would play a game of chess. Whoever lost the game owed a chocolate to the other. After the last game we played (that was the day she was to leave), we counted the number of games each of us had won and lost. Wow! I had won more than her. So, she handed me 25 chocolates... though she herself was the winner in 5 games.
How many days did my cousin spend at my place?
The Pink Wooden Block
A block of wood in the form of a cuboid 5" x 10" x 11" has all its six faces painted pink. If the wooden block is cut into 550 cubes of 1" x 1" x 1", how many of these would have pink paint on them?
Spiders on the Web
"Dad, where had you been?" asked Andy.
"I had been to the attic, my son," replied Dad. "And do you know what I saw there? There was a big web with 21 spiders and flies on it."
"How many spiders were there?" asked the little boy with curiosity.
"Well, there were a total of 132 legs on the web," answered Dad with a smile. "Now you can find out how many spiders were there by yourself. Can't you?"
Can you help the little boy find out how many spiders were on the web in the attic?
Unique Numbers
There is a number that is 8 times the sum of its digits. What is this number?
Speeding Away
The drive from Oakland to Pinewood was a tricky one. I covered the uphill distance of 70 miles at 35 miles per hour. The return journey from Pinewood to Oakland was downhill, and I managed to drive at 63 miles per hour. What was my average speed for the entire journey?
Tennis Championship
A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.
(a) How many players participate in the tournament if 127 matches are totally played?
(b) How many matches are played in the tournament if 55 players totally participate?
Old Enough ?
Mark:
"When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 5 years from now?"
Gold Coins
A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?"
After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 61 times the difference between the two numbers equals the difference between the squares of the two numbers."
The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?
The Snake in the Hole
A snake slides through a long cylindrical hole in the ground at 6 centimetres per second. The hole is 7.56 metres in length. The snake takes 16 seconds to enter the hole.
(a) What is the length in centimetres of the snake ?
(b) How many seconds does the snake take to exit the hole after entering it?
At a Tangent
Consider 7 lines drawn at a tangent to an ellipse. The lines break up the plane into several regions, some bounded (i.e., enclosed) and others unbounded. How many unbounded regions are there?
Football Matches
A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once.
If 21 matches are totally played, how many teams participated?
Heavy Enough ?
Bodo weighs 80 pounds more than his sister, Stacy. Their combined weight is 100 pounds. How many pounds does Bodo weigh?
Vacation Time
It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long.
Now, there were 16 mornings when we did nothing, 18 evenings when we stayed at home, and a total of 16 days when we jogged or played tennis. For how many days did I stay at my cousin's place?
Fill it Up
A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 2 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 8 hours.
What fraction of the tank (initially empty) will be filled in 0.46 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
Pyramids of Egypt
My Dad has a miniature Pyramid of Egypt. It is 4 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 8) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.
If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.
The Creeper on the Tree
A creeper plant is climbing up and around a cylindrical tree trunk in a helical manner. The tree trunk has a height of 480 inches and a circumference of 32 inches.
If the creeper covers a vertical distance of 60 inches in one complete twist around the tree trunk, what is the total length of the creeper?
The Great Pizza Deal
The 8" pizza sells for $ 5.99 at my favorite pizza store. The store claims they have a great deal on the large 14" pizza, which is specially priced at $ 13.76. What is the per cent discount the store is offering?
Grandpa's Age
Grandpa:
"My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?"