Can You Solve the Mystery of the Tape Recorder Riddle?

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In summary, the scientists were given a symbol to which they had to guess the meaning. If they got it right, they earned a point. If they were wrong, they lost a point. The head of the scientist position decided who was the most intelligent of the three based on their points.
  • #71
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.
 
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  • #72
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.
 
  • #73
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
 
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  • #74
Jimmy is correct. Good Job! You get the next puzzle.
 
  • #75
whew! :biggrin:
 
  • #76
j-j-j-j-jimmay!
 
  • #77
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.
 
  • #78
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.
 
  • #79
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?
 
  • #80
Space?...
 
  • #81
no, it's a lot harder.
 
  • #82
Earth?...
 
  • #83
warmer, still pretty far off
 
  • #84
It's a sphere
 
  • #85
jimmy got it, but he's not really doing this so people keep guessing
 
  • #86
a box might fit ?
 
  • #87
sorry...boxes aren't curved
 
  • #88
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.
 
  • #89
BicycleTree said:
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. :mad:
 
  • #90
yomamma said:
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.
 
  • #91
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 infinately 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
 
  • #92
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?
 
  • #93
heartache and headache?
 
  • #94
Yes, you're up.
 
  • #95
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.
 
  • #96
turn the light on... :-p
 
  • #97
DarkEternal said:
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.
 
  • #98
that will take a long time in the dark
 
  • #99
nice tries, but no. there's no trick answer...
 
  • #100
yomamma said:
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.
 
  • #101
DarkEternal said:
nice tries, but no. there's no trick answer...
What? That's totally a valid way to do it! No trick, just thinking outside the box.
 
  • #102
Actually I think Dave's got "the" answer that's supplied with that riddle. There might be other ways, though.
 
  • #103
I finally figured it out! :biggrin: You have to grab half of the pennies (5) and flip them all over. If you picked up all tails and made that one group, there will be 5 heads after flipping them, and 5 heads in the other group (the rest of the pennies). If you pick up 4 tails and 1 head, that will be 4 heads and 1 tail, and the rest will be 4 heads and one tail; if you pick up 3 tails and 2 heads, there will be 2 tails and 3 heads, and the rest will have that, and so on all the way to if you pick up all the heads, flipped them to tails, and the rest will be tails. That way there will always be the same number of heads in each group.
 
  • #104
I was so stupid to miss that one.
 
  • #105
nice one calc...go ahead!
 

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