Can You Solve the Mystery of the Tape Recorder Riddle?

[Berislav]

Sorry it took me this long to reply.

Good work, Icebreaker. Your turn.

 

[Icebreaker]

ICEBREAKER! *slaps icebreaker* other people were supposed to solve the riddle, not you!

Well that was certainly odd.

Good work, Icebreaker. Your turn.

Find a counterexample to the Riemann hypothesis.

Just kidding. Here's an easy one:

The length of the perimeter of a right triangle is 60 and the length of its altitude perpenticular to the hypotenuse is 12. Find the sides and show your work.

Good luck.

 

[Moo Of Doom]

The length of the perimeter of a right triangle is 60 and the length of its altitude perpenticular to the hypotenuse is 12. Find the sides and show your work.

Let a and b denote the lengths of the legs of the triangle, and let c denote the length of the hypotenuse.

60=a+b+c
a^2+b^2=c^2
ab/2=12c/2

Solving this system of equations, we get

a=15
b=20
c=25

 

[Icebreaker]

Yup. Your turn.

 

[JamesU]

Okay, moo of doom, your turn

 

[Moo Of Doom]

Yikes, I don't really have anything...

Here goes...
Find the next row in this sequence:

1
2, 1
3, 3, 2, 1
4, 4, 4, 3, 2, 1
5, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
?

 

[JamesU]

6, 5, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1


I'm really not sure, I took a huge guess

 

[Moo Of Doom]

Nope.

I'll give you a hint: it's more than twice as long as the last one. (sorry :P)

 

[JamesU]

Can you give a bigger hint?

 

[Moo Of Doom]

There are 62 numbers in the sequence, and the highest number in the sequence is 32, which is repeated 17 times.

There's another big hint I'm willing to give if it's absolutely necessary.

 

[JamesU]

does it involve adding, subtraction, mult... you get it, so does it?

 

[Moo Of Doom]

It involves subtraction, but not in the way you think. It also involves addition, but in an even weirder way than the subtraction.

(Basically, if you think the pattern is anything akin to add one, subtract two, etc. you're on the wrong track. There is no such rule, really.)

 

[Moo Of Doom]

I have the feeling this puzzle is a bit too freakishly difficult, so here comes a big hint:

The sequence is very closely related to this one:

1
10, 1
11, 10, 2, 1
100, 11, 10, 3, 2, 1
...
?

If you're still stuck, I'll give the fifth row of the above sequence, although it kind of gives it away.

 

[JamesU]

30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

 

[Moo Of Doom]

You have part of it, but you're missing the first 12 numbers, and one of the 32s.

 

[JamesU]

18, 19, 20, 21, 22, 23, 24, 25,, 26, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

 

[Moo Of Doom]

You have it right from 24 on, but the bit before that is wrong.
Think about how the first sequence might relate to the second sequence, and see if that helps. Tell me if you want the next row for the second sequence.

 

[JamesU]

20, 21, 22, 23, 24, 25, 24, 25,, 26, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

 

[Moo Of Doom]

Nope, colder.

 

[JamesU]

I give up, give another.

 

[Moo Of Doom]

Here's the original sequence:

1
2, 1
3, 3, 2, 1
4, 4, 4, 3, 2, 1
5, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Here's the second sequence:

1
10, 1
11, 10, 2, 1
100, 11, 10, 3, 2, 1
101, 100, 22, 21, 20, 15, 14, 13 , 12, 11, 10, B, A, 9, 8, 7, 6, 5, 4, 3, 2, 1

Two entries in the last row should be a big hint as to what kind of problem this is. How do these sequences relate? Dividing into columns may help.

 

[Jimmy Snyder]

To get the original sequence from the second sequence: find the representation in base 10 for each number in a row assuming that the number in the nth column is represented in base (n + 1). For instance, in the last row 101 base 2 is 5 base 10, 100 base 3 is 9 base 10, 22 base 4 is 10 base 10, 21 base 5 is 11 base 10, etc.
But I don't yet see how to get the second sequence.

 

[Jimmy Snyder]

Now I see how to get the second sequence.

101 -1 (base 2) = 100
100 -1 (base 3) = 22
22 - 1 (base 4) = 21
21 - 1 (base 5) = 20
20 - 1 (base 6) = 15
etc.
So the next line in the second sequence is:
110, 101, 100, 33, 32, 31, 30, 27, 26, 25, 24, 23, 22, 21, 20, 1F, 1E, 1D, 1C, 1B, 1A, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, V, U, T, S, R, Q, P, O, N, M, L, K, J, I, H, G, F, E, D, C, B, A, 9, 8, 7, 6, 5, 4, 3, 2, 1

Converting to the original sequence we get:

6, 10, 16, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, ..., 32, 31, 30, ..., 1

 

[Moo Of Doom]

Jimmy is correct. Good Job! You get the next puzzle.

 

[JamesU]

whew!

 

[JamesU]

j-j-j-j-jimmay!

 

[Jimmy Snyder]

It is now my turn to propose a puzzle. I do not intend to do so. I mean no disrespect, but I sincerely hope that this thread will not continue. The reason is that when there is one puzzle per thread, we can more easily reference the puzzles. I'm sorry if I offend, and I open the floor to anyone who has a puzzle to propose and doesn't want it to show up in the forum in a thread of its own.

 

[Moo Of Doom]

The point of this forum is mostly to share interesting puzzles and to challenge each other to figure them out, not to catalogue brain teasers. If it were, it'd have more than 2 pages and my binary sequence thread will still be on here. This thread in particular, was created purely to have some fun, and to add some incentive to solving puzzles. I, for one, hope this thread lasts a while. (By the way, there are similar threads in General Physics and General Math)

Anyone's turn for a puzzle. I had the last one, I'm not taking it.

 

[JamesU]

Curved when I'm small
Flat when I'm all
Infanite is all
big, wide and tall

I extend in three directions
a paridox of perplexions

What am I?

 

[Huckleberry]

Space?...

 

[JamesU]

no, it's a lot harder.

 

[Huckleberry]

Earth?...

 

[JamesU]

warmer, still pretty far off

 

[Jimmy Snyder]

It's a sphere[/color]

 

[JamesU]

jimmy got it, but he's not really doing this so people keep guessing

 

[ArielGenesis]

a box might fit ?

 

[JamesU]

sorry...boxes[/color] aren't curved

 

[BicycleTree]

There is already a thread for this type of thing (one of the stickies, in fact) and it was abandoned. When each puzzle has a link of its own you can reference them better. Not store them, reference them. You can go straight to the puzzle you want when it has its own link.

 

[icvotria]

There is already a thread for this type of thing (one of the stickies, in fact) and it was abandoned. When each puzzle has a link of its own you can reference them better. Not store them, reference them. You can go straight to the puzzle you want when it has its own link.

I like this thread. It's GREAT. You get new riddles quicker than you would if it wasn't here. Big deal if you can't reference them, you get lots and it's fun. Anyway, someone already brought this point up, you don't have to make it again. I can't answer this riddle though cos I already looked at the answer. I find it really hard not to look at the things in white.

 

[Icebreaker]

Curved when I'm small
Flat when I'm all
Infanite is all
big, wide and tall

I extend in three directions
a paridox of perplexions

What am I?

Um... a closed 4-sphere? So it extends in 3 dimensions but still "curves" in 4-space, and "infinite" in 3-space.

 

[JamesU]

I guess you got it. the correct answer was a sphere.

Flat when I'm all infanite is all. all=infanite. as a circular object gets bigger, the curvature of it's circumfrence decreases to the observer. (just look at earth.) so an infinate[/color]ly large circular object would be flat.

so now it could either be a circle or sphere... lines four and five give you the idea of 3 directions. so 3 dimensions. it's a sphere

 

[Icebreaker]

Mmm... a riddle... here's an easy one:

He starts and ends 2 common English words. One painfull in love, one painfull in everyday matter. Do you know what 2 words I must be?

 

[DarkEternal]

heartache and headache?

 

[Icebreaker]

Yes, you're up.

 

[DarkEternal]

you have 10 pennies on a desk, 5 heads up and 5 tails up. the room is dark so you cannot distinguish between them. split the pennies into 2 groups, each with the same number of heads up. you are allowed to flip the pennies, but you can't cheat by feeling them.

 

[JamesU]

turn the light on...

 

[DaveC426913]

you have 10 pennies on a desk, 5 heads up and 5 tails up. the room is dark so you cannot distinguish between them. split the pennies into 2 groups, each with the same number of heads up. you are allowed to flip the pennies, but you can't cheat by feeling them.

Assuming yoyoama's answer isn't it, I know how I can do it:
Place all 10 pennies on edge. You can divide them into two groups however you want, each group will still have 0 pennies heads up.

 

[JamesU]

that will take a long time in the dark

 

[DarkEternal]

nice tries, but no. there's no trick answer...

 

[DaveC426913]

that will take a long time in the dark

Why? How would being able to see help you do that? It's totally tactile. Actually, it's REALLY easy to do if you simply stack 5 pennies together, then merely lie the stack on its side.