4 ms·

An exercise in riddle-solving

14 points by techdog 17y ago

deleted 17y ago
[deleted]
alexgartrell 17y ago
my guess was pi :(
jpwagner 17y ago
it jumps out right away that: 1+1+1+1+1 = 5 2+2+2+2+2 = 10 and 1+0 = 1 3+3+3+3+3 = 15 and 1+5 = 6 (whenever it's sums of digits you think mod 9) since there are 5 numbers, the sum of the coefficients mod 9 = 5 (ie, 5, 14, 23...) that's as far as I went before giving up anyone got the rest without brute force? ---------------------------------------------- Oh and what's with the author's justification of random guessing?
- req2 17y ago
  The author also thinks the birthday paradox doesn't apply to his hashes and that the assumptions an interviewer grants to an interview question can't be taken for granted. The author takes a dim view of convention. http://news.ycombinator.com/item?id=605126 http://news.ycombinator.com/item?id=605126
- tspiteri 17y ago
  From 1 1 1 1 1 = 5 1 1 1 1 2 = 1 1 1 1 1 3 = 6 1 1 1 1 4 = 2 ... you can see that an increase of 1 in the last digit will increase the answer by 5 or decrease it by 4, so it is an increase of 5 mod 9. Similarly, from 1 1 1 1 1 = 5 2 1 1 1 1 = 8 3 1 1 1 1 = 2 4 1 1 1 1 = 5 ... you can see that an increase of 1 in the first digit will increase the answer by 3 or decrease it by 6, so it is an increase of 3 mod 9. So the first digit is multiplied by 3 and the last digit is multiplied by 5. That rings a bell, since the last line is 3 1 4 1 5, which starts with a 3 and ends with a 5, so you must suspect that the second digit should be multiplied by 1, the third by 4, and the fourth by 1. Go over a few numbers, or all of the numbers, to check this out, and it works, so you can apply it to the last line and get the answer.
  - jpwagner 17y ago
    since the last line is 31415 That would be brute force,,,
    - tspiteri 17y ago
      There's a reason why the puzzle-writer used those 5 digits in the final question, so that you can spot the pattern and find a shortcut. Spotting the pattern is not brute force. To check your formula you have to do some calculations, but that is something you cannot avoid. By going over the numbers, what I mean is confirming that: 1x3 + 2x1 + 3x4 + 4x1 + 5x5 = 1 5x3 + 4x1 + 3x4 + 2x1 + 1x5 = 2 ... You can do that manually or mentally, so it is not what I call brute force. And if you do not spot the 3 1 4 1 5 pattern, or just do not want to use the shortcut provided, there is another way to do it. First let's find the second digit. We only need our known digits and the two lines 2 2 2 2 2 = 1 1 1 2 2 2 = 6 Since we know that the multiplier of the first digit is 3, we can calculate the value of 1 2 2 2 2 = 2 2 2 2 2 - 1 0 0 0 0 = 1 - 3 = 7. Then it follows that the multiplier of the second digit is 1 2 2 2 2 - 1 1 2 2 2 = 7 - 6 = 1. The third digit can be found by changing the line 1 2 3 4 5 = 1 to 3 3 3 4 4 = 3. You can do this since you have the multipliers for the first, second and fifth digits. We already have the line 3 3 4 4 4 = 7, so the third digit is 7 - 3 = 4. For the fourth multiplier, change the line 1 1 1 1 1 = 5 to 2 2 2 1 2 = 0. Compare to 2 2 2 2 2 = 1 and you see that the fourth multiplier is 1. So now you have all the five multipliers, 3, 1, 4, 1 and 5. But we are not necessarily ready yet, we may need to add a constant, c. So pick a line, the easiest seems to be 1 1 1 1 1 = 5. Now, since we know the five multipliers, we can say that 1x3 + 1x1 + 1x4 + 1x1 + 1x5 + c = 5 5 + c = 5 c = 0 The constant is 0. So just multiplying each digit by its respective multiplier gives the correct answer. You still need to verify your formula by calculating the right hand side of a few lines.
- rw 17y ago
  Deciding whether or not to guess depends on the consequences of being wrong.
gjm11 17y ago
Although the author says he solved it, he didn't; he made a guess and got lucky. Perhaps there's a subtle joke going on? (Or maybe it's not so subtle and I'm just being dim. Then again, I solved the puzzle in a couple of minutes and he apparently didn't.) I don't think it's a terribly interesting puzzle.
- scott_s 17y ago
  I upvoted the submission not for the puzzle, but the author's discussion after it.
- lhorie 17y ago
  His point is that he got the value of "?", but not the "correct" method to arrive at that solution. Neither of blog posts seem to ask explicitly for the method. I think choosing to take a statistical gamble on a silly meaningless puzzle (rather than attempt to solve it conventionally like everyone else) is actually not necessarily a bad idea. I talked about that a while back here : http://lhorie.blogspot.com/2009/03/games-bias-and-statistics.html http://lhorie.blogspot.com/2009/03/games-bias-and-statistics... (albeit I was reacting to a more statistical-natured puzzle at that time) I do agree this puzzle isn't very interesting in that it doesn't evoke as much gut feeling as, say, the Monty Hall paradox.

14 points by techdog 17y ago

deleted 17y ago

[deleted]

alexgartrell 17y ago

my guess was pi :(

jpwagner 17y ago

it jumps out right away that: 1+1+1+1+1 = 5 2+2+2+2+2 = 10 and 1+0 = 1 3+3+3+3+3 = 15 and 1+5 = 6 (whenever it's sums of digits you think mod 9) since there are 5 numbers, the sum of the coefficients mod 9 = 5 (ie, 5, 14, 23...) that's as far as I went before giving up anyone got the rest without brute force? ---------------------------------------------- Oh and what's with the author's justification of random guessing?

req2 17y ago
The author also thinks the birthday paradox doesn't apply to his hashes and that the assumptions an interviewer grants to an interview question can't be taken for granted. The author takes a dim view of convention. http://news.ycombinator.com/item?id=605126 http://news.ycombinator.com/item?id=605126
tspiteri 17y ago
From 1 1 1 1 1 = 5 1 1 1 1 2 = 1 1 1 1 1 3 = 6 1 1 1 1 4 = 2 ... you can see that an increase of 1 in the last digit will increase the answer by 5 or decrease it by 4, so it is an increase of 5 mod 9. Similarly, from 1 1 1 1 1 = 5 2 1 1 1 1 = 8 3 1 1 1 1 = 2 4 1 1 1 1 = 5 ... you can see that an increase of 1 in the first digit will increase the answer by 3 or decrease it by 6, so it is an increase of 3 mod 9. So the first digit is multiplied by 3 and the last digit is multiplied by 5. That rings a bell, since the last line is 3 1 4 1 5, which starts with a 3 and ends with a 5, so you must suspect that the second digit should be multiplied by 1, the third by 4, and the fourth by 1. Go over a few numbers, or all of the numbers, to check this out, and it works, so you can apply it to the last line and get the answer.
- jpwagner 17y ago
  since the last line is 31415 That would be brute force,,,
  - tspiteri 17y ago
    There's a reason why the puzzle-writer used those 5 digits in the final question, so that you can spot the pattern and find a shortcut. Spotting the pattern is not brute force. To check your formula you have to do some calculations, but that is something you cannot avoid. By going over the numbers, what I mean is confirming that: 1x3 + 2x1 + 3x4 + 4x1 + 5x5 = 1 5x3 + 4x1 + 3x4 + 2x1 + 1x5 = 2 ... You can do that manually or mentally, so it is not what I call brute force. And if you do not spot the 3 1 4 1 5 pattern, or just do not want to use the shortcut provided, there is another way to do it. First let's find the second digit. We only need our known digits and the two lines 2 2 2 2 2 = 1 1 1 2 2 2 = 6 Since we know that the multiplier of the first digit is 3, we can calculate the value of 1 2 2 2 2 = 2 2 2 2 2 - 1 0 0 0 0 = 1 - 3 = 7. Then it follows that the multiplier of the second digit is 1 2 2 2 2 - 1 1 2 2 2 = 7 - 6 = 1. The third digit can be found by changing the line 1 2 3 4 5 = 1 to 3 3 3 4 4 = 3. You can do this since you have the multipliers for the first, second and fifth digits. We already have the line 3 3 4 4 4 = 7, so the third digit is 7 - 3 = 4. For the fourth multiplier, change the line 1 1 1 1 1 = 5 to 2 2 2 1 2 = 0. Compare to 2 2 2 2 2 = 1 and you see that the fourth multiplier is 1. So now you have all the five multipliers, 3, 1, 4, 1 and 5. But we are not necessarily ready yet, we may need to add a constant, c. So pick a line, the easiest seems to be 1 1 1 1 1 = 5. Now, since we know the five multipliers, we can say that 1x3 + 1x1 + 1x4 + 1x1 + 1x5 + c = 5 5 + c = 5 c = 0 The constant is 0. So just multiplying each digit by its respective multiplier gives the correct answer. You still need to verify your formula by calculating the right hand side of a few lines.
rw 17y ago
Deciding whether or not to guess depends on the consequences of being wrong.

gjm11 17y ago

Although the author says he solved it, he didn't; he made a guess and got lucky. Perhaps there's a subtle joke going on? (Or maybe it's not so subtle and I'm just being dim. Then again, I solved the puzzle in a couple of minutes and he apparently didn't.) I don't think it's a terribly interesting puzzle.

scott_s 17y ago
I upvoted the submission not for the puzzle, but the author's discussion after it.
lhorie 17y ago
His point is that he got the value of "?", but not the "correct" method to arrive at that solution. Neither of blog posts seem to ask explicitly for the method. I think choosing to take a statistical gamble on a silly meaningless puzzle (rather than attempt to solve it conventionally like everyone else) is actually not necessarily a bad idea. I talked about that a while back here : http://lhorie.blogspot.com/2009/03/games-bias-and-statistics.html http://lhorie.blogspot.com/2009/03/games-bias-and-statistics... (albeit I was reacting to a more statistical-natured puzzle at that time) I do agree this puzzle isn't very interesting in that it doesn't evoke as much gut feeling as, say, the Monty Hall paradox.