Hint: If your hot tap fills up your bath at the rate of half a gallon every five minutes, your cold tap two thirds of an acre every three minutes and your plug is draining at five square centimetres every half an hour, it will take John seventy three minutes to drive to Coventry at an twelve miles an hour.
Ah good - I did wonder if the initial numbers were relevant to the sequence (i.e. if they themselves were part of some Fibionacci sequence or somesuch guff)
Well it’s partly about how people test hypothesis. So I was expecting people to throw sequences at me to figure out what the requirements are. If people don’t throw sequences at me I can only tell them they are wrong if they try jump straight to the definition of the sequence.
So if you said
2.2 &mdash 4.4 &mdash 5.4
I would say wrong. And by testing different sequences you should be able to figure out the rules restricting the sequences.
Perhaps I should have been more distinct in what I expected, but I wanted to see how people reacted to something that was deliberately vague, and how they go about investagting the sequence.
Incorrect. But finally a sequence that reveals something. Diamond Geezer gets a gold star. For brilliance and I think it’s the first time he has commented here.
Am I right in thinking that positive integers are called ‘whole numbers’ and that this doesn’t include zero? So maybe I should have said x - 2x - (2x)+1 where X is a whole number?
Showing that there are other approaches to the same conundrum… (if this is a training exercise, it might conceivably being about showing that ‘there is more than one valid approach to a problem, man.’ (long drag on bong, settle back into bean bag)
Natural number can mean either a positive integer (1, 2, 3, 4, …) or a non-negative integer (0, 1, 2, 3, 4, …).
The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, …) and the number zero. They are also known as the whole numbers, although that term is also used to refer only to the positive integers (with or without zero).
Either way you’re still wrong. In all of your answers.
To be fair, there was no indication that more than three examples of the sequence were required in order to solve this problem.
If we are going to be really pedantic about testing the boundaries of the problem space how are we to know that the series is just three numbers long.
We have all given answers which are correct based on the evidence presented to us which means that all answers so far are correct. Whether they are correct for all x [and incidentally, in a series of unknown length, with an unknown starting point what member of the series do you take as x?] is unknown to us since there are seemingly further restrictions on the problem which have not been divulged.
Is this a problem solvable in its entirity based upon evidence presented or is it a guessing game?
David, you have all given answers that fit the evidence that is correct. No one has really started to test the problem space except Diamond Geezer. The problem is solved entirely by testing hypothesis. The initial state of testing a hypothesis is often guessing. However it’s using those guesses to refine your hypothesis where the guessing stops. It should only be guessing in the early stages.
Tol, the course was on how to manage people better. This was about 10 minutes out of a day and a half of the course.
Yep. That’s it. Three whole numbers in a row with each number bigger than the last.
Well done, you win the prize. Well if there was a prize.
I’m going to close comments on this now, because I want to keep the discussion separate, for the sake of readability. If you want to make any comments on this test please comment on my follow on post: Challenging preconceived notions. I welcome all comments and discussion. I’ve only closed comments on this to try keep the discussion in one place. Not to avoid criticism.
1. graybo
House! Where’s my prize?
2. Adrian
What? No.
Give me other examples of the same sequence.
3. David
1673 - 3346 - 3345
4. david
arrggghhh i did it wrong, the last number should be 3347
5. Green Fairy
5656568 - 11313136 - 11313137
Are you stuck on the Mensa test or something?
Hint: If your hot tap fills up your bath at the rate of half a gallon every five minutes, your cold tap two thirds of an acre every three minutes and your plug is draining at five square centimetres every half an hour, it will take John seventy three minutes to drive to Coventry at an twelve miles an hour.
6. Adrian
David, first one wrong (obviously) correction right.
Green Fairy, correct. No, not Mensa, it was something done at yesterdays training. Am curious to see how people respond to it.
John couldn’t get to Coventry as they were doing road works and he turned back.
7. Lyle
1 - 2 - 3 ?
It certainly follows the rules as I’ve figured them so far…
8. Adrian
Correct.
9. Lyle
Ah good - I did wonder if the initial numbers were relevant to the sequence (i.e. if they themselves were part of some Fibionacci sequence or somesuch guff)
However, my theory has been proved. grin
10. Adrian
Nope. Three random examples, of the sequence. But nice to see people (well you) testing hypothesis out.
11. Green Fairy
And this trained you for what, exactly?
12. David
So what was the purpose of the excercise?
To see if people overcomplicate things or look for bigger problems than there actually are?
13. Adrian
I’ll wait a while before explaining the sequences. I want to see what other examples people put forward.
14. Nuge
x - 2x - 2x+1
15. Adrian
Incorrect. Does not hold true for all values of X.
16. David
Are you looking for a formula that defines the series?
17. Adrian
I’m looking for what the series is. This can be defined as a formulae or in words.
18. David
….prepares to be told he’s wrong….
is it:
mod (x) — 2mod (x) — 2mod (x) +1
19. Adrian
Incorrect. Does not hold true for all values of X.
20. Pete
No, but it certainly holds true for all the examples that you’ve given, so it’s most unfair of you to tell people that they are wrong.
I’m guessing that the additional requirement is that x is an integer?
21. Adrian
Well it’s partly about how people test hypothesis. So I was expecting people to throw sequences at me to figure out what the requirements are. If people don’t throw sequences at me I can only tell them they are wrong if they try jump straight to the definition of the sequence.
So if you said
2.2 &mdash 4.4 &mdash 5.4
I would say wrong. And by testing different sequences you should be able to figure out the rules restricting the sequences.
Perhaps I should have been more distinct in what I expected, but I wanted to see how people reacted to something that was deliberately vague, and how they go about investagting the sequence.
22. diamond geezer
-1 - -2 - -1 (if that isn’t dashed overload)
23. Adrian
Incorrect. But finally a sequence that reveals something. Diamond Geezer gets a gold star. For brilliance and I think it’s the first time he has commented here.
24. diamond geezer
Blimey - was that really my first time? Still, this doubles it…
25. diamond geezer
… and this adds one more.
26. Adrian
Always glad when someone pops that sevitzdotcom cherry.
27. Coop
x - 2x - 2x+1 For all x where x>0
28. Adrian
Incorrect.
29. diamond geezer
0 - 0 - 1
30. Adrian
Incorrect.
31. Tol
Quoting Coop “x - 2x - 2x+1 For all x where x>0” AND X is an integer?
32. Adrian
Nope.
33. Tol
Am I right in thinking that positive integers are called ‘whole numbers’ and that this doesn’t include zero? So maybe I should have said x - 2x - (2x)+1 where X is a whole number?
34. Tol
Showing that there are other approaches to the same conundrum… (if this is a training exercise, it might conceivably being about showing that ‘there is more than one valid approach to a problem, man.’ (long drag on bong, settle back into bean bag)
.5(y-1) - y-1 - y
35. Adrian
Natural number can mean either a positive integer (1, 2, 3, 4, …) or a non-negative integer (0, 1, 2, 3, 4, …).
The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, …) and the number zero. They are also known as the whole numbers, although that term is also used to refer only to the positive integers (with or without zero).
Either way you’re still wrong. In all of your answers.
36. David
To be fair, there was no indication that more than three examples of the sequence were required in order to solve this problem.
If we are going to be really pedantic about testing the boundaries of the problem space how are we to know that the series is just three numbers long.
We have all given answers which are correct based on the evidence presented to us which means that all answers so far are correct. Whether they are correct for all x [and incidentally, in a series of unknown length, with an unknown starting point what member of the series do you take as x?] is unknown to us since there are seemingly further restrictions on the problem which have not been divulged.
Is this a problem solvable in its entirity based upon evidence presented or is it a guessing game?
37. Tol
This training course you’re on wouldn’t be about getting the best out of staff you manage, would it? Just a thought.
38. Adrian
David, you have all given answers that fit the evidence that is correct. No one has really started to test the problem space except Diamond Geezer. The problem is solved entirely by testing hypothesis. The initial state of testing a hypothesis is often guessing. However it’s using those guesses to refine your hypothesis where the guessing stops. It should only be guessing in the early stages.
Tol, the course was on how to manage people better. This was about 10 minutes out of a day and a half of the course.
39. Pete
Ooh! I know! It’s x - 2x - 2x+1 where x is 1, 2, 3, 14, 1673 or 5656568.
Manage THAT, motherfucker.
40. Lyle
Have you been watching Pulp Fiction again, Pete?
41. David
Are all examples of the series 3 numbers long?
42. Dav
Does the series you have apply to all numbers (positive, negative, rational, irrational, imaginary)?
43. Adrian
I’m not answering specific questions about the numbers, and I’ll only confirm if a series given is correct or incorrect.
44. David
making the rules up as you go along!
45. Adrian
Incorrect. I haven’t changed the rules since the begenning.
46. Stuart
-3 -2 -1?
47. Adrian
Correct.
48. Stuart
121 - 456 - 987
49. Adrian
Correct.
50. Stuart
So is it simply any series of ascending whole numbers?
51. Adrian
Yep. That’s it. Three whole numbers in a row with each number bigger than the last.
Well done, you win the prize. Well if there was a prize.
I’m going to close comments on this now, because I want to keep the discussion separate, for the sake of readability. If you want to make any comments on this test please comment on my follow on post: Challenging preconceived notions. I welcome all comments and discussion. I’ve only closed comments on this to try keep the discussion in one place. Not to avoid criticism.