WIL RIDDLES WITH ANSWERS TO SOLVE - PUZZLES & BRAIN TEASERS

An echo. Did you answer this riddle correctly?
YES  NO  

First the farmer takes the rabbit across and returns to the fox & cabbage. Next, the farmer takes the cabbage, but when he arrives to the other side with the rabbit, he leaves the cabbage and takes the rabbit back on the raft with him to return and get the fox. He exchanges the rabbit for the fox and returns to drop the fox off with the cabbage, and finally goes back to get the rabbit. Did you answer this riddle correctly?
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His nose did grow when he said it would, but his nose is only supposed to grow when he lies, and his nose would grow even though he told the truth, and the paradox appears to exist again.

You can prove that's not true because he created a self fulfilling prophecy when he said his nose was going to grow bigger because saying that was saying he was going to lie.

In order to lie; he had to tell the truth, and say that he was lying, when he was really telling the truth, which would be a lie.

He did say he was lying because he said his nose was going to grow, and even though he said he was lying, he was actually telling the truth; which means he was lying about lying, or lying about not telling the truth.

His nose did grow, and he did tell the truth, but he said he was lying when he was telling the truth, which was the lie that made his nose grow.

Since his nose didn't grow after he told the truth, but after he lied about not telling the truth; the paradox doesn't exist.

That second answer actually works for both scenarios, where as the first answer only works for the first scenario, so I suppose you can say the second answer is the correct one. Did you answer this riddle correctly?
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A fire. Did you answer this riddle correctly?
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Current Future Past

Princess x 2z (x+y)/2
Prince y x z

I then created three equations, since the difference in their age will always be the same.

d = the difference in ages

x y = d
2z x = d
x/2 + y/2 z = d

I then created a matrix and solved it using row reduction.

x y z

1 -1 0 d
-1 0 2 d
.5 .5 -1 d

It reduced to:

x y z

1 0 0 4d
0 1 0 3d
0 0 1 5d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).

Princess age: 4d
Prince age: 3d

Ages that work

Princess:
4
8
16
24
32
40
48
56
64
72
80

Prince:
3
6
12
18
24
30
36
42
48
54
60 Did you answer this riddle correctly?
YES  NO  

A centipede Did you answer this riddle correctly?
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DAVID (Roman numerals) Did you answer this riddle correctly?
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There is a 50/50 chance of each toss being either heads or tails. The previous toss does not impact the next toss. Did you answer this riddle correctly?
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Clover Did you answer this riddle correctly?
YES  NO  

Santa Did you answer this riddle correctly?
YES  NO  

Dreidel Did you answer this riddle correctly?
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Mirror Did you answer this riddle correctly?
YES  NO  

Thanksgiving Day Did you answer this riddle correctly?
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Cornucopia Did you answer this riddle correctly?
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October Did you answer this riddle correctly?
YES  NO