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[SFW] Riddles / Puzzles / Brain Teasers - Page 4

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TheAngryZergling
Profile Joined January 2011
United States387 Posts
Last Edited: 2012-04-18 16:12:45
April 18 2012 16:11 GMT
#61
On April 19 2012 00:22 DarkPlasmaBall wrote:
Riddle 1:

What is the next line of numbers?

**********1**********
********1***1********
********2***1********
****1***2***1***1****
1***1***1***2***2***1

Solution:
+ Show Spoiler +
312211, and here's why:

You *read off* the previous row, matching numbers that are alike and together in the preceding row, to come up with the next row. You say how many of each number there are, in order.

Row two: Row one is "one one".
Row three: Row two is "two ones"
Row four: Row three is "one two, one one".
Row five: Row four is "one one, one two, two ones".
Therefore, Row six: Row five is "three ones, two twos, one one", or 312211.



I'd say that riddle is ambiguous since the following solution also works:
+ Show Spoiler +

**************1**************
************1***1************
************2***1************
********1***2***1***1********
****1***1***1***2***2***1****
2***1***1***1***3***2***1***1

Arrived at by the following.
Apply 1 of the following rules listed in order of precedence with tokens processed left to right:
- for a pair of consecutive #s add 1 to the leftmost
- otherwise add a 1 to the left of that #

Though of course the listed solution is more riddle-esque.
Everything in life is most clearly explained through a Starcraft analogy.
danl9rm
Profile Blog Joined July 2009
United States3111 Posts
April 18 2012 16:11 GMT
#62
On April 19 2012 00:10 solidbebe wrote:
Show nested quote +
On April 19 2012 00:08 DarkPlasmaBall wrote:
Here's a riddle:

How do you know when someone cheats and looks online for the solution to a riddle?

+ Show Spoiler +
On April 18 2012 23:33 sc2system wrote:
you are presented with 2 doors. one has millions of dollars behind it and the other has a lion that will eat you behind it. there are 2 guards in front of the doors that know what is behind the doors. one of them always tells the truth and one of them always lies, but you don't know which is which. You can only ask one question. What do you ask?


Took me like 2 minutes.

Solution:
+ Show Spoiler +
You ask "What would your brother say if I asked him behind which door the million dollars are?".

You will get the door where the dragon is.






Hahahaha I was thinking this, when did the lion become a dragon?


Ahhhhahahahaha. Emmmbarrassing.
"Science has so well established that the preborn baby in the womb is a living human being that most pro-choice activists have conceded the point. ..since the abortion proponents have lost the science argument, they are now advocating an existential one."
TheAngryZergling
Profile Joined January 2011
United States387 Posts
April 18 2012 16:14 GMT
#63
On April 19 2012 00:24 WarEagle wrote:
I remember these from the Dark Tower 3: The Waste Lands

What has a mouth but cannot talk,
has legs but cannot walk,
has a head but cannot think,
has a bed but never sleeps.

+ Show Spoiler +
A river


A loose translation:
It's more powerful than God.
It's more evil than the Devil.
The poor have it.
The rich need it.
If you eat it you will die.

+ Show Spoiler +
Nothing


Dark Tower series FTW. Having my wife read through those currently. Sooo good.
Everything in life is most clearly explained through a Starcraft analogy.
summerloud
Profile Joined March 2010
Austria1201 Posts
April 18 2012 16:18 GMT
#64
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]
HotShizz
Profile Blog Joined May 2011
France710 Posts
Last Edited: 2012-04-18 16:22:27
April 18 2012 16:18 GMT
#65
On April 19 2012 00:53 DarkPlasmaBall wrote:
Show nested quote +
On April 19 2012 00:50 Cocacooh wrote:
On April 19 2012 00:24 WarEagle wrote:
I remember these from the Dark Tower 3: The Waste Lands

What has a mouth but cannot talk,
has legs but cannot walk,
has a head but cannot think,
has a bed but never sleeps.

+ Show Spoiler +
A river


A loose translation:
It's more powerful than God.
It's more evil than the Devil.
The poor have it.
The rich need it.
If you eat it you will die.

+ Show Spoiler +
Nothing


+ Show Spoiler +
Couldnt figure out the first one, I didnt get the leg part. Whats a "rivers leg" can't figure it out ?


I always heard it as "I bend but have no legs", so I just disregarded that line. Does that make more sense?


+ Show Spoiler +
Just around the riverbend!!!


+ Show Spoiler +
In fact, if I am not mistaken, it runs but it has no legs


All time greatest riddle

What do I have in my pocket?

*edit quote fail
DarkPlasmaBall
Profile Blog Joined March 2010
United States45338 Posts
Last Edited: 2012-04-18 16:20:03
April 18 2012 16:19 GMT
#66
On April 19 2012 01:18 HotShizz wrote:
Show nested quote +
On April 19 2012 00:53 DarkPlasmaBall wrote:
On April 19 2012 00:50 Cocacooh wrote:
On April 19 2012 00:24 WarEagle wrote:
I remember these from the Dark Tower 3: The Waste Lands

What has a mouth but cannot talk,
has legs but cannot walk,
has a head but cannot think,
has a bed but never sleeps.

+ Show Spoiler +
A river


A loose translation:
It's more powerful than God.
It's more evil than the Devil.
The poor have it.
The rich need it.
If you eat it you will die.

+ Show Spoiler +
Nothing


+ Show Spoiler +
Couldnt figure out the first one, I didnt get the leg part. Whats a "rivers leg" can't figure it out ?


I always heard it as "I bend but have no legs", so I just disregarded that line. Does that make more sense?

+ Show Spoiler +
In fact, if I am not mistaken, it runs but it has no legs


All time greatest riddle

What do I have in my pocket?

+ Show Spoiler +
Just around the riverbend!!!



You posted your comment in my quote >.> lol I didn't say that.

Never mind, you fixed it
"There is nothing more satisfying than looking at a crowd of people and helping them get what I love." ~Day[9] Daily #100
SomniGiggles
Profile Joined May 2011
United Kingdom214 Posts
April 18 2012 16:19 GMT
#67
As I was going to St Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
Kits, cats, sacks, wives.
How many were going to St Ives?
DarkPlasmaBall
Profile Blog Joined March 2010
United States45338 Posts
Last Edited: 2012-04-18 16:21:05
April 18 2012 16:20 GMT
#68
On April 19 2012 01:19 SomniGiggles wrote:
As I was going to St Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
Kits, cats, sacks, wives.
How many were going to St Ives?


+ Show Spoiler +
Just you One.
"There is nothing more satisfying than looking at a crowd of people and helping them get what I love." ~Day[9] Daily #100
sc2system
Profile Joined February 2012
Bangladesh55 Posts
Last Edited: 2012-04-18 16:23:59
April 18 2012 16:22 GMT
#69
[image loading]

Solution:

+ Show Spoiler +
It seems that the other triangle is not as high as the other one so I guess that there the 1 blank sport comes form. Only a guess, I work on a very old small dark screen so I might see it wrong I go and check once more



EDIT: WRONG
sc2system
Profile Joined February 2012
Bangladesh55 Posts
Last Edited: 2012-04-18 16:26:26
April 18 2012 16:23 GMT
#70
On April 19 2012 01:19 SomniGiggles wrote:
As I was going to St Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
Kits, cats, sacks, wives.
How many were going to St Ives?


+ Show Spoiler +
You only mentioned yourself. This one probably only works if you read it to someone.
endy
Profile Blog Joined May 2009
Switzerland8970 Posts
Last Edited: 2012-04-18 16:25:51
April 18 2012 16:24 GMT
#71
On April 19 2012 01:18 summerloud wrote:
Show nested quote +
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.


Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]


+ Show Spoiler +
None of the "assembled" shapes are triangle. What we would call hypotenuse in one shape is concave, while the other is convex. That was tricky haha.
ॐ
midgettoes
Profile Joined June 2010
Australia180 Posts
April 18 2012 16:29 GMT
#72
On April 19 2012 01:24 endy wrote:
Show nested quote +
On April 19 2012 01:18 summerloud wrote:
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.


Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]


+ Show Spoiler +
None of the "assembled" shapes are triangle. What we would call hypotenuse in one shape is concave, while the other is convex. That was tricky haha.


+ Show Spoiler +

Correct. The easiest way to see it is to look at the 2nd bottom row, where the 'hypotenuse' is (ie left most of 2nd row). One image has a complete square there, one has the top corner slightly clipped by white space. That's how I convinced myself anyway.
TheAngryZergling
Profile Joined January 2011
United States387 Posts
Last Edited: 2012-04-18 16:34:48
April 18 2012 16:32 GMT
#73
On April 19 2012 01:22 sc2system wrote:
Show nested quote +
[image loading]

Solution:

+ Show Spoiler +
It seems that the other triangle is not as high as the other one so I guess that there the 1 blank sport comes form. Only a guess, I work on a very old small dark screen so I might see it wrong I go and check once more



EDIT: WRONG


actually ...
+ Show Spoiler +

thats basically right. The issue is that since the triangles have different ratios of height to length they don't form a true triangle. so the hypotenuse of the first is slightly 'bulged' outwards and the second is inwards. its just hard to discern that visually.


edit: nm I misread your guess, w/out relating the height and width of the 2 triangle pieces that isn't quite an acceptable solution.
Everything in life is most clearly explained through a Starcraft analogy.
endy
Profile Blog Joined May 2009
Switzerland8970 Posts
April 18 2012 16:33 GMT
#74
On April 19 2012 01:29 midgettoes wrote:
Show nested quote +
On April 19 2012 01:24 endy wrote:
On April 19 2012 01:18 summerloud wrote:
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.


Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]


+ Show Spoiler +
None of the "assembled" shapes are triangle. What we would call hypotenuse in one shape is concave, while the other is convex. That was tricky haha.


+ Show Spoiler +

Correct. The easiest way to see it is to look at the 2nd bottom row, where the 'hypotenuse' is (ie left most of 2nd row). One image has a complete square there, one has the top corner slightly clipped by white space. That's how I convinced myself anyway.



+ Show Spoiler +
Well thanks to the grid, you see quickly that triangles don't have the same angles. It would be much much harder if instead of the grid it was simply saying that both shapes are 13 cm wide and 5 cm high.
ॐ
sc2system
Profile Joined February 2012
Bangladesh55 Posts
Last Edited: 2012-04-18 16:35:41
April 18 2012 16:35 GMT
#75
On April 19 2012 01:33 endy wrote:
Show nested quote +
On April 19 2012 01:29 midgettoes wrote:
On April 19 2012 01:24 endy wrote:
On April 19 2012 01:18 summerloud wrote:
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.


Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]


+ Show Spoiler +
None of the "assembled" shapes are triangle. What we would call hypotenuse in one shape is concave, while the other is convex. That was tricky haha.


+ Show Spoiler +

Correct. The easiest way to see it is to look at the 2nd bottom row, where the 'hypotenuse' is (ie left most of 2nd row). One image has a complete square there, one has the top corner slightly clipped by white space. That's how I convinced myself anyway.



+ Show Spoiler +
Well thanks to the grid, you see quickly that triangles don't have the same angles. It would be much much harder if instead of the grid it was simply saying that both shapes are 13 cm wide and 5 cm high.


+ Show Spoiler +
Sorry for this post but it says no where that each square is 1cm x 1cm. So it basically 5 units high and 13 units high
Geo.Rion
Profile Blog Joined October 2008
7377 Posts
April 18 2012 16:36 GMT
#76
On April 18 2012 23:44 Ghanburighan wrote:
[image loading]

+ Show Spoiler [Hint] +
Count something


+ Show Spoiler [solution] +
Count the number of circles in the numbers, for example 8 has two.

damn, i arrived at the right conclusion,+ Show Spoiler +
2, but didnt notice it has anything to do with circles, i simply noticed the numbers have a "weight" most of them 0, so i went on and discovered 6, 9, 0 had a "weight" of one, and 8 has "2".
"Protoss is a joke" Liquid`Jinro Okt.1. 2011
Kimaker
Profile Blog Joined July 2009
United States2131 Posts
April 18 2012 16:43 GMT
#77
On April 19 2012 00:34 Mentalizor wrote:
Don't know if you know this - but a teacher told it to me 7 years ago. So it's probably ancient. So here goes:
(it was another currency but in order not to confuse too much, let's use dollars)
The riddle:
+ Show Spoiler +
3 men enter a bar. They order 3 beers that all cost 10$, so the men give the waitress 30$.
However when she goes up to the bartender and tells him to get 3 beers and hands over the 30$ he says: Oh no, we have a special offer with 3 beers for 25$. So now the waitress has to go back with 5$. But you can't split 5$ into 3. So she takes 2$ for herself and hands the gentlemen their beers and 1$ each.

So this adds up. Doesn't it? Or wait... Now they all paid 9$ - so 9$ * 3 = 27$... And the waitress took 2$ for herself. That's 29$. Where did the last dollar go?


The hint:

+ Show Spoiler +
Pay attention to who are paying for what and the actual prices


The solution:

+ Show Spoiler +
There is no missing dollar. The men were to pay 25$ and the waitress took 2$ for herself. Meaning the men paying 27$ is the correct amount. It's a common deception to just add up all the money instead of realizing the actual numbers are from different points of view.


Hope you liked it

+ Show Spoiler +
It breaks a rule in the order of operations. There is no missing dollar.
Entusman #54 (-_-) ||"Gold is for the Mistress-Silver for the Maid-Copper for the craftsman cunning in his trade. "Good!" said the Baron, sitting in his hall, But Iron — Cold Iron — is master of them all|| "Optimism is Cowardice."- Oswald Spengler
Strykemard
Profile Joined April 2012
168 Posts
Last Edited: 2012-04-18 17:25:19
April 18 2012 17:24 GMT
#78
On April 19 2012 01:18 summerloud wrote:
Show nested quote +
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]



+ Show Spoiler +
You can solve this by looking closely. Instead of thinking of the triangles as replacing each other, think of them as being extended to fit the description.

The sizes are 5x2 and 8x3.

So to replace the smaller triangle by the bigger one, you need to extend it by one vertical box, and 2 horizontal boxes. However, we see that if we extend it, it doesnt fit in with the grid.

Basically, while the two triangles seem to form a straight line to the naked eye, they aren't actually straight. The smaller triangle has a slightly higher angle ( i.e, the hypotenuse is closer to the horz line ) and reverse for the bigger triangle. So, in the second case, the paritions are eating some space outside of what the first diagram did. Because the volume doesn't change, it is compensated by a "hole" inside.


solidbebe
Profile Blog Joined November 2010
Netherlands4921 Posts
April 18 2012 17:27 GMT
#79
On April 19 2012 02:24 Strykemard wrote:
Show nested quote +
On April 19 2012 01:18 summerloud wrote:
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]



+ Show Spoiler +
You can solve this by looking closely. Instead of thinking of the triangles as replacing each other, think of them as being extended to fit the description.

The sizes are 5x2 and 8x3.

So to replace the smaller triangle by the bigger one, you need to extend it by one vertical box, and 2 horizontal boxes. However, we see that if we extend it, it doesnt fit in with the grid.

Basically, while the two triangles seem to form a straight line to the naked eye, they aren't actually straight. The smaller triangle has a slightly higher angle ( i.e, the hypotenuse is closer to the horz line ) and reverse for the bigger triangle. So, in the second case, the paritions are eating some space outside of what the first diagram did. Because the volume doesn't change, it is compensated by a "hole" inside.



+ Show Spoiler +

And this is why I think it's a horrible riddle. Since it's not about thinking of a smart solution to solve it. The maker of the riddle intentionally deceives you with something very small and you just need to be very observant to notice.
That's the 2nd time in a week I've seen someone sig a quote from this GD and I have never witnessed a sig quote happen in my TL history ever before. -Najda
TheAngryZergling
Profile Joined January 2011
United States387 Posts
April 18 2012 17:45 GMT
#80
On April 19 2012 02:27 solidbebe wrote:
Show nested quote +
On April 19 2012 02:24 Strykemard wrote:
On April 19 2012 01:18 summerloud wrote:
On April 19 2012 01:01 Rob28 wrote:
Riddle: You are in a room with three light switches, each of which connects to a lightbulb in an adjacent room that you cannot see into. You do not know which switch goes with which bulb. You may only leave the switch room and can never re-enter it. How do you tell which switch controls which bulb?

Non-spoilered kinda hint: This puzzle involves no clever wordplay in it's description that is indicative of the solution. So don't try to solve it by reading too much into it.

Will post solution after seeing some guesses.


this is really old. but there are a lot of solutions to it:

+ Show Spoiler +

solution 1 (normal one): turn on switch 1 for an hour, turn it off, turn on switch 2, go see which lamp is hot and which one is turned on now

solution 2 (creative one): turn on all the switches in any order and go to the other room above light speed so you can see in which order they turn on



but much better than either of these solutions: what would feynmann do? (solution spoilered at the very end)

hereis my riddle, its also kinda old, might post solution later:

[image loading]



+ Show Spoiler +
You can solve this by looking closely. Instead of thinking of the triangles as replacing each other, think of them as being extended to fit the description.

The sizes are 5x2 and 8x3.

So to replace the smaller triangle by the bigger one, you need to extend it by one vertical box, and 2 horizontal boxes. However, we see that if we extend it, it doesnt fit in with the grid.

Basically, while the two triangles seem to form a straight line to the naked eye, they aren't actually straight. The smaller triangle has a slightly higher angle ( i.e, the hypotenuse is closer to the horz line ) and reverse for the bigger triangle. So, in the second case, the paritions are eating some space outside of what the first diagram did. Because the volume doesn't change, it is compensated by a "hole" inside.



+ Show Spoiler +

And this is why I think it's a horrible riddle. Since it's not about thinking of a smart solution to solve it. The maker of the riddle intentionally deceives you with something very small and you just need to be very observant to notice.


Its not the best but as mentioned by another poster, the answer doesn't hinge entirely on visual observation. However, a bit of math background is required which is why this is usually found in geometry books or the like (at least thats where I recall seeing it o so long ago).
Everything in life is most clearly explained through a Starcraft analogy.
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