An interesting maths puzzle

In summary, a common puzzle involves finding the odd ball out of 8 balls using a two-sided weight scale and 3 tries. A similar puzzle involves determining which of two cannonballs will hit the ground first, given one is dropped from 4 miles off the ground and the other is shot from a cannon and travels 4 miles before it hits the ground. There are variations in the problem due to factors such as air density and drag, but the key is to realize that the height of the balls does not matter and the dropped ball will always hit last. This puzzle has been discussed in various forms and can be found online.
  • #1
Recently, my friend tested me on a puzzle. The puzzle goes like this, if there is 8 balls (1 of them which weighs either lesser or heavier), how are you going to find out which is the different ball using a two sided weight scale with 3 tries?

This is a pretty easy puzzle which everyone would solve given enough time. After giving it some thought, I realized I can not only find which is the different ball with 3 tries but also tell whether it is heavier or lighter then the rest.

How do I do it?
 
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  • #2
icyboy771z said:
Recently, my friend tested me on a puzzle. The puzzle goes like this, if there is 8 balls (1 of them which weighs either lesser or heavier), how are you going to find out which is the different ball using a two sided weight scale with 3 tries?

This is a pretty easy puzzle which everyone would solve given enough time. After giving it some thought, I realized I can not only find which is the different ball with 3 tries but also tell whether it is heavier or lighter then the rest.

How do I do it?

This is actually a very common puzzle. A bit of Googling will reveal the answer as well as many variations on it.
 
  • #3
It commonly done with 12 balls.

number the balls

weigh 1,2 against 3,4
1. if they balance, the 5,6,7,8 has the odd one - weigh 123 vs 567
- if 123 vs 567 balance then 8 is the odd one (weigh against any other for heavy/light.
- if 567 is heavy, then they contain the heavy ball, weigh 5 vs 6: if 5 vs 6 balance, then 7 is heavy otherwise the heavier of 5,6 is the odd ball.
- if 567 is light then they contain the light ball - as above.

2. 1,2 vs 3,4 not balanced then 5,6,7,8 are all the same - weigh 1,2,3 vs 5,6,7
- if balanced then 4 is the odd one
- if 123 > 567 then the odd one is heavy, weigh 1 vs 2
- if 123 < 567 then the odd one is light, weigh 1 vs 2

Try this one:
http://trickofmind.com/2008/11/cannon-ball-conundrum.html

A cannon ball is shot out of a cannon and travel 4 miles before it hits the ground, at the same time a cannon ball is dropped out of the sky 4 miles off the ground

The question is Which Cannon ball will hit the ground first, Explain


I've seen it in different versions, here's a discussion:
http://simonbjournal.blogspot.com/2011/06/cannon-balls.html
 
Last edited:
  • #4
Simon Bridge said:
It commonly done with 12 balls.

number the balls

weigh 1,2 against 3,4
1. if they balance, the 5,6,7,8 has the odd one - weigh 123 vs 567
- if 123 vs 567 balance then 8 is the odd one (weigh against any other for heavy/light.
- if 567 is heavy, then they contain the heavy ball, weigh 5 vs 6: if 5 vs 6 balance, then 7 is heavy otherwise the heavier of 5,6 is the odd ball.
- if 567 is light then they contain the light ball - as above.

2. 1,2 vs 3,4 not balanced then 5,6,7,8 are all the same - weigh 1,2,3 vs 5,6,7
- if balanced then 4 is the odd one
- if 123 > 567 then the odd one is heavy, weigh 1 vs 2
- if 123 < 567 then the odd one is light, weigh 1 vs 2

Try this one:
http://trickofmind.com/2008/11/cannon-ball-conundrum.html

A cannon ball is shot out of a cannon and travel 4 miles before it hits the ground, at the same time a cannon ball is dropped out of the sky 4 miles off the ground

The question is Which Cannon ball will hit the ground first, Explain


I've seen it in different versions, here's a discussion:
http://simonbjournal.blogspot.com/2011/06/cannon-balls.html

with regards to the cannonball problem, the "travel 4 miles" is problemmatic. is this the arc-length of the projectory, vertical travel, or horizontal travel?

and of course, there's variations in air density, coefficients of drag, the fact that 4 miles is enough away from the surface of the Earth to affect the acceleration, it's...ugly.

if it is one of the famous acme frictionless cannonballs, and the various vagaries of drag, air density, non-constant acceleration, etc. are ignored, AND we only mean the vertical travel of the cannonball, then they hit at the same time.
 
  • #5
Yeah - that's why I linked to my earlier observations along the same lines.

Some versions have the height at 10 miles. The large heights lead me to suspect that the cannon firing may be intended as a red herring - the lynchpin may be to realize that here is a situation where it does not matter how the cannon is fired. The dropped ball starts so far up it always hits last?

Retellings garbled the numbers.

Have a google about - you'll see it keeps cropping up as a brain-teaser.
 

1. What is the puzzle about?

The puzzle is a math problem that requires logical thinking and problem-solving skills to find the solution.

2. How difficult is the puzzle?

The difficulty level of the puzzle can vary depending on the person's math abilities. Some may find it easy, while others may find it challenging. However, with practice and patience, anyone can solve it.

3. Is there only one correct answer?

Yes, there is only one correct solution to the puzzle. However, there may be different approaches or methods to reach the answer.

4. Can the puzzle be solved by anyone?

Yes, anyone can solve the puzzle with basic math skills and critical thinking. It may require some trial and error, but ultimately, it can be solved by anyone.

5. What is the benefit of solving the puzzle?

Solving puzzles can improve critical thinking, problem-solving, and logical reasoning skills. It can also be a fun and challenging activity for those interested in math and puzzles.

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