Brain Teasers
Reverse Engineering II
The formula discovered in "Reverse Engineering I" doesn't seem to apply exactly to many Braingle ratings once the number of voters gets larger. What is your best guess at the number of votes cast for each attribute of the following teasers prior to my vote, and how many of those were positive (fun/hard)? What do you think is the likely source of any "experimental error" between the formula and these reported ratings? (Notation is the same as in "Reverse Engineering I"). Multiple answers may be possible, because of the difficulty of determining how much of the reported data constitutes "experimental error."
Teaser M: (1.38, 1.20)[16] (+, -) -> (1.53, 1.13)
Teaser N: (2.00, 2.22)[18] (+, -) -> (2.11, 2.11)
Teaser O: (1.04, 2.82)[25] (-, +) -> (1.00, 2.87)
Teaser P: (2.13, 1.72)[44] (+, -) -> (2.17, 1.68)
Teaser M: (1.38, 1.20)[16] (+, -) -> (1.53, 1.13)
Teaser N: (2.00, 2.22)[18] (+, -) -> (2.11, 2.11)
Teaser O: (1.04, 2.82)[25] (-, +) -> (1.00, 2.87)
Teaser P: (2.13, 1.72)[44] (+, -) -> (2.17, 1.68)
Answer
The formula from part I, for p positive votes out of v cast, was 4*p/v. I searched for fractions with denominators close to the reported number of voters and numerators that were multiples of 4 to try to find a good fit. Here are some of the best possibilities, with the resulting decimals reported below. Divide numerators by 4 to get the number of positive votes.Teaser M: (16/12, 16/13)[16] (+, -) -> (20/13, 16/14)
(1.33, 1.23)[16] (+, -) -> (1.54, 1.14). It's hard to find a good match for this one. Another possibility is 20/15->24/16 (1.33->1.5) for the first rating, which is further off from the data, but doesn't require as many non-voters.
Teaser N: (36/18, 40/18)[18] (+, -) -> (40/19, 40/19)
(2.00, 2.22)[18] (+, -) -> (2.11, 2.11) An exact match to the data.
Teaser O: (24/23, 68/24)[25] (-, +) -> (24/24, 72/25)
(1.04, 2.83)[25] (-, +) -> (1.00, 2.88) Pretty close.
Teaser P: (92/43, 72/42)[44] (+, -) -> (96/44, 72/43)
(2.14, 1.71)[44] (+, -) -> (2.18, 1.67) Off by .01 in every figure.
The above errors (particularly on Teaser M) would be hard to account for if the site were recomputing the ratings every time from p and v. We know that the site keeps track of v for each category, in order to qualify entries for the various lists. But the site may recalculate p every time from the previous (rounded) ranking, which could cause errors that could accumulate or cancel, depending on how unlucky/lucky you were about what order people voted in. This could account for the errors in the above data. If this is the problem, the best fix would be to keep a separate count of p for each ranking. A temporary fix would be to at least round p off to the nearest integer when deriving it from the previous ranking, which works up to around 200 votes or so.
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Comments
what happened to 'no self refenceing tesasers'?
if there is a bad "Teaser M: (16/12, 16/13)[16] (+, -) -> (20/13, 16/14)
(1.33, 1.23)[16] (+, -) -> (1.54, 1.14). It's hard to find a good match for this one. Another possibility is 20/15->24/16 (1.33->1.5) for the first rating, which is further off from the data, but doesn't require as many non-voters.
Teaser N: (36/18, 40/1[18] (+, -) -> (40/19, 40/19)
(2.00, 2.22)[18] (+, -) -> (2.11, 2.11) An exact match to the data.
Teaser O: (24/23, 68/24)[25] (-, +) -> (24/24, 72/25)
(1.04, 2.83)[25] (-, +) -> (1.00, 2.8 Pretty close.
Teaser P: (92/43, 72/42)[44] (+, -) -> (96/44, 72/43)
(2.14, 1.71)[44] (+, -) -> (2.18, 1.67) Off by .01 in every figure." Teaser then I havent seen it.
(1.33, 1.23)[16] (+, -) -> (1.54, 1.14). It's hard to find a good match for this one. Another possibility is 20/15->24/16 (1.33->1.5) for the first rating, which is further off from the data, but doesn't require as many non-voters.
Teaser N: (36/18, 40/1[18] (+, -) -> (40/19, 40/19)
(2.00, 2.22)[18] (+, -) -> (2.11, 2.11) An exact match to the data.
Teaser O: (24/23, 68/24)[25] (-, +) -> (24/24, 72/25)
(1.04, 2.83)[25] (-, +) -> (1.00, 2.8 Pretty close.
Teaser P: (92/43, 72/42)[44] (+, -) -> (96/44, 72/43)
(2.14, 1.71)[44] (+, -) -> (2.18, 1.67) Off by .01 in every figure." Teaser then I havent seen it.
just to let you all know..... i hate math riddles!!!!!!!!!!!!
I think that formula is something simple, like (example for Difficulty, same is for Fun): if number of all casted votes N= N_easy +N_middle +N_hard, then
avg= (N_middle*2 + N_hard*4) / N
and any small differences are probably due to rounding of displayed result, where 3rd decimal digit is not shown.
Above formula takes into consideration something that seems overlooked in posted answers both for Reverse I and Reverse II : value if someone cast middle vote.
As an example that covers teaser (1.33, 1.23)[16] (+, -) -> (1.54, 1.14) .... if we look only Difficulty part, we voted positive and from 1.33 got to 1.54. Since we dont know what was N here (N N=12 And that means we had 12 people out of those 16 vote on difficulty before our last vote. Those 12 people votes resulted in 1.33 score, and with above formula, there are several options for that : #1: 4 hard+8 easy #2: 2 hard+ 4 medium+ 4 easy etc
avg= (N_middle*2 + N_hard*4) / N
and any small differences are probably due to rounding of displayed result, where 3rd decimal digit is not shown.
Above formula takes into consideration something that seems overlooked in posted answers both for Reverse I and Reverse II : value if someone cast middle vote.
As an example that covers teaser (1.33, 1.23)[16] (+, -) -> (1.54, 1.14) .... if we look only Difficulty part, we voted positive and from 1.33 got to 1.54. Since we dont know what was N here (N N=12 And that means we had 12 people out of those 16 vote on difficulty before our last vote. Those 12 people votes resulted in 1.33 score, and with above formula, there are several options for that : #1: 4 hard+8 easy #2: 2 hard+ 4 medium+ 4 easy etc
At the time I created this teaser (and Revers Engineering), the "middle" vote was not an option - your choices were to vote up, down, or not vote in each of the two categories. I imagine the formula has changed a bit in recent years.
Mar 19, 2005
too hard
Mar 19, 2005
too hard
Mar 19, 2005
too hard
Mar 19, 2005
too hard
If you think the teaser was too hard, feel free to rate it as difficult (lots of people already have, if you look at the rating). If it being too difficult spoiled your fun, you can rate it as boring (or neutral, depending on how generous you feel). If you want to say *why* you thought it was too hard, or what in particular you had difficulty with, that might lead to an interesting discussion.
But just telling us four times that
you thought it was "too hard" doesn't
really add much, I'm afraid. Not every teaser is for everyone. Feel free to use the categories and ratings to find teasers that you enjoy more.
But just telling us four times that
you thought it was "too hard" doesn't
really add much, I'm afraid. Not every teaser is for everyone. Feel free to use the categories and ratings to find teasers that you enjoy more.
wow i could not get this one... even after looking at the answer...
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