Puzzle #131: The Pyramid Problem

Posted on February 21, 2016 by Alok Goyal

This is a beautiful geometry puzzle contributed by my nephew, Karan Sharma. The puzzle originally appeared in a PSAT exam in 1980, and was not really a “puzzle” until one student proved that there was a different answer than what everyone had thought. Enough in already!

Here it goes – A tetrahedron and a pyramid with edges of unit length are glued together at one triangular face. How many exposed faces does the resulting solid have?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy geometry day!

Posted in Puzzles | Tagged , | 3 Comments

Solution to Puzzle #129: The Einstein’s Puzzle

Posted on February 21, 2016 by Alok Goyal

I got many answers for this puzzle, I think the title attracted quite a few people. First person to send the correct answer was Radhika Goyal, just ahead of her dad (Deepak Goyal), who was 10 minutes behind her. Others to send the correct answers included Sid Mulherkar, Vikas Jangra, Rahul Rane, Amit Jain and Suman Saraf (who wrote a Python script to figure out all the possible permutations!).

The method is a bit manual, a process of elimination of possibilities with the constraints given. The answer is:

The Norwegian drinks water.
The Japanese owns zebra .

The full table is as follows:

Einstein's Puzzle Solution

Einstein’s Puzzle Solution

Hope you all enjoyed the puzzle!

 

 

Posted in Solution | Tagged , | Leave a comment

Puzzle #130: The Plato Riddle

Posted on February 14, 2016 by Alok Goyal

I am on a roll here with the old-time biggies, after Einstein we have Plato now! This is a beautiful puzzle and riddle contributed by Sirisha Gadepalli, an IIT Campus friend – thank you Sirisha!

Here it goes:

Aristotle was the prized student of Plato, and the good thing was that they never had to sit in classrooms, all the learning was outside the class. But the boring part was that Plato was the only teacher, so he would teach everything and mix up different subjects together, basically there was no maths period, or science period or social studies period.
One day while walking together, Plato and Aristotle had the conversation below.

——————all that matters begins here—————————–

Plato: a square be square, a cube be cube.
Aristotle: well isn’t it obvious?
Plato(smiles): And they both combine to give a circle.
Aristotle: that’s so deep.
Plato(smirks): But a square is not circle, and let circle not be square.
Aristotle(irritatingly): so, whats the question?
Plato(after a while): what is a bee?
Aristotle: what?????????
Plato (takes a deep breath): Close your eyes Aristotle, and repeat what I said. What stops you from answering the question is your failure to identify that one negativity which you are not realizing.

————Nothing else matters——————————————

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy Valentine Day to all of you!

 

 

Posted in Puzzles | Tagged , , | 6 Comments

Solution to Puzzle #128: The Milkman Again

Posted on February 14, 2016 by Alok Goyal

Apologies for not posting last weekend, I was traveling, and am likely to be traveling quite a bit in the next month, so there will be some irregularity in posting.

This was a relatively simple one, lots of people sent correct answers that included Pratik Poddar, Aditya GV, P R Kumar, Suman Saraf, Arjun Raychaudhuri, Shruti Mittal, Girish Tutakne, Anubhav Garg and Abhishek Masand. Well done all!

There is clearly more than one way to do it, I am reproducing the one from Girish Tutakne.

Let us name the jars A (for 24 lit), B (13 lit), C(11 Lit) and D(5 lit). I will use the nomenclature for example A(10) to represent that jar A has 10 lit of milk.
Initial condition: A(24); B(0); C(0); D(0)
Step 1: A(8); B(0); C(11); D(5) —-> poured milk from jar A to fill up jars C and D
Step 2: A(8); B(13); C(0); D(3) —-> poured milk first from jar C completely and then remainder from jar D to fill up jar B
Step 3: A(8); B(13); C(3); D(0) —-> poured milk from jar D to jar C
Step 4: A(8); B(8); C(3); D(5) —-> poured mils from jar B to fill up jar D
Step 5: A(8); B(8); C(8); D(0) —-> poured milk from jar D to jar C. We now have 3 jars with 8 lit each

Hope you all enjoyed the puzzle!

 

Posted in Solution | Tagged , | Leave a comment

Puzzle #129: The Einstein’s Puzzle

Posted on January 31, 2016 by Alok Goyal

I am sure the title will catch everyone’s attention. It is a very cute puzzle that Einstein invented as a child. The puzzle is also attributed to Lewis Carroll. There are many versions of this puzzle, the one here is copied from Wikipedia, and originally from Life International in 1962.

So here it goes for all the budding Einsteins!

  1. There are five houses.
  2. The Englishman lives in the red house.
  3. The Spaniard owns the dog.
  4. Coffee is drunk in the green house.
  5. The Ukrainian drinks tea.
  6. The green house is immediately to the right of the ivory house.
  7. The Old Gold smoker owns snails.
  8. Kools are smoked in the yellow house.
  9. Milk is drunk in the middle house.
  10. The Norwegian lives in the first house.
  11. The man who smokes Chesterfields lives in the house next to the man with the fox.
  12. Kools are smoked in the house next to the house where the horse is kept.
  13. The Lucky Strike smoker drinks orange juice.
  14. The Japanese smokes Parliaments.
  15. The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra?

In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarets. One other thing: in statement 6, right means your right.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy playing with the Zebra!

 

 

Posted in Puzzles, Uncategorized | Tagged , | 2 Comments

Solution to Puzzle #127: Building and Eggs Again

Posted on January 31, 2016 by Alok Goyal

This was a difficult puzzle, and I did not get any complete answer from anyone. Ofcourse, Alok Aggarwal, who contributed the puzzle, had an answer. I will replicate the answer I gave to Alok.

The answer is 8, i.e. within a maximum of 8 trials, you can figure out which is the lowest floor on which the egg can break. Here is the explanation:

– First identify one of the three 27 floor segments by trying from 27th and 54th respectively (if it breaks from 27th, then we do not need to try 54th, if it does not break even in the 54th, we know that it is the last segment)
– Then identity the segment of 9 floors within the identified 27, by trying 9 floors from the beginning of the segment, e.g. if the egg broke on 54th, we should try 27+9. i.e. 36th floor, and then 45th floor
– then identify the segment of 3
– finally identify the segment of 1

In each case one will need to make maximum of 2 tries, and hence 8.

Hope you all enjoyed the puzzle!

Posted in Solution, Uncategorized | Tagged , | Leave a comment

Puzzle #128: The Milkman Again

Posted on January 17, 2016 by Alok Goyal

Almost 3 years back, I had posted a milkman puzzle, which was the second puzzle I posted (https://alokgoyal1971.com/2013/02/10/solution-to-puzzle-2-milkman-puzzle/). Here again is a modified version of the same puzzle. A very interesting puzzle that Alok Mittal gave to his Mathematical Circles class.

A milkman has four jars of the following sizes – 24 litres, 13 litres,  11 litres and 5 litres. The 24 litre jar is full of milk, and the others are empty. He needs to divide the milk into three parts of 8 litres each. Unfortunately, the milkman has no additional markings in the existing jars to be able to figure out how to measure 8 litres. Can you help the milkman?

Please send your answers either directly on the blog site as comments, or to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

Happy dividing!

Posted in Puzzles, Uncategorized | Tagged , | 6 Comments

Solution to Puzzle #126: The Tricky Square Root

Posted on January 17, 2016 by Alok Goyal

Again received an overwhelming number of answers to this puzzle. People who answered it correctly included Pratik Poddar, Anant Aggarwal, Siddharth Mulherkar, Suman Saraf, P R Kumar and Amit Mittal. The puzzle had a simple trick to it, which is that the phrase we are trying to get to is embedded itself within the phrase.

I am reproducing the answer from Pratik Poddar.

Lets say that the value is x.
sqrt (12+x) = x
x^2 – x – 12 = 0
(x-4)(x+3) = 0
x = 4 (since x>0)

Hope you all enjoyed the puzzle!

 

Posted in Solution, Uncategorized | Tagged , | 2 Comments

Puzzle #127: Building and Eggs Again

Posted on January 10, 2016 by Alok Goyal

This is a wonderful puzzle shared by a good friend Alok Aggarwal, who lives in California and are a family of math wizards (which includes him as well!).

This puzzle is a variation of puzzle #94  (https://alokgoyal1971.com/2015/03/01/puzzle-94-two-eggs-and-a-building/), where with two eggs and a building with 100 floors, one had to figure out an optimal strategy for finding the lowest floor at which an egg will break when dropped. Optimality is defined by least number of trials.

For the same problem, assume you have 81 floors and 4 eggs, what is the optimal strategy?

Happy egging again!

Posted in Puzzles | Tagged , | 1 Comment

Solution to Puzzle #125: Test Your Creativity

Posted on January 10, 2016 by Alok Goyal

I was overwhelmed not only by the response, but also by the creativity. While I do not like to single people out, Suman Saraf turned out to be the champion of creativity on this one, had some remarkable variations that I have not seen even on the original source I took the puzzle from (brilliant.org).

The most common answer that Anant Aggarwal, Rahul Rane, Pratik Poddar and Suman Saraf sent me were:

1 + 4! – 9 – 16 (for children, 4! = 1 x 2 x 3 x 4)

Aditya Geevee and Suman Saraf also sent me the following one, which required modification of the right side as well, which most people did not try:

1 – √4 + √9 = √16  (√ stands for square root)

A very good variation of the above sent by Prakhar Prakash:

1 + 4 – √9 = √√16 (means square root of square root of 16)

The cake, as I said, goes to Suman Saraf though for three more variations:

(1 * 4) % 9 = √16 where % is modulo

⎣(√√√(1+4)! * 9)⎦ = 16    i.e. floor(sqrt(sqrt(sqrt((1+4)!))) * 9)

My favourite one from Suman:

1/4% – 9 = 16

I loved the answers, hope you all enjoyed this puzzle!

Posted in Solution | Tagged , | Leave a comment