Logic Problem

[RATATTAK]

V8LM said:

2nd weighing is take three from the left and put on the right, take three from the right and put on the table, and take three from the table on put on the left.

Well done, you've got it down to one of three and you know if it's heavier or lighter and the third weighing is easy

second weighing

sss^ l ^^^v

RHS goes up it's one of ^^^ and it's lighter

Scale balances it's one of vvv (on the table) and it's heavier

[Strudul]

Hard to work with text and keep track of things, much easier when you draw it out.

This is a little clearer than my scribbles though:

[anonymous-user]

Strudul said:

Hard to work with text and keep track of things, much easier when you draw it out.

This is a little clearer than my scribbles though:

Was thinking divide into sets of 4 for the first, because it allows you to eliminate a group that you know for certain doesn't contain the faulty item. Then I went for three on the next step because you can, again, eliminate some entirely. I figure, wrongly, at the third step that you'd only be able to get it down to two potential suspects, needing a fourth step to pinpoint one.

[lj04]

5 on both sides if the same heavier is matchstick leftover. If not take the heavier group of 5 , 2 on each scale if the same, heavier matchstick is one leftover. If not take the heavier group of 2 I think you can guess the rest.

[RATATTAK]

lj04 said:

5 on both sides if the same heavier is matchstick leftover. If not take the heavier group of 5 , 2 on each scale if the same, heavier matchstick is one leftover. If not take the heavier group of 2 I think you can guess the rest.

Have you taken into account that it could be lighter ?

[FarmyardPants]

My attempt, probably flawed. Didn't read the spoiler.

Measure 4 each side
If it balances
  You have 8 standards 
  measure 3 standards with 3 of the remaining.
  If that Balances
    Measure the 4th against one of the standards
  Else
    (If the non-standard side went down/up,
    you have 1 heavier/lighter)
    Measure any two of the 3, one each side
Else
  You have ABCD on one side and EFGH on the other
  Say ABCD went down
  Measure ABEF against CDSS (S = standard)
  If it balances
    Measure G and H, whichever goes up is lighter
  Else If ABEF goes down
         A or B is heavier, so measure A vs B
  Else if CDSS goes down
         C or D is heavier, so measure C vs D
  Similarly if EFGH went down

[FarmyardPants]

Took about half an hour to figure out, hope it's valid!?

doesn't identify the cases of E or F being lighter, doh!

Edited by FarmyardPants on Tuesday 16th January 14:16

[blinkythefish]

FarmyardPants said:

My attempt, probably flawed. Didn't read the spoiler.

Measure 4 each side
If it balances
  You have 8 standards 
  measure 3 standards with 3 of the remaining.
  If that Balances
    Measure the 4th against one of the standards
  Else
    (If the non-standard side went down/up,
    you have 1 heavier/lighter)
    Measure any two of the 3, one each side
Else
  You have ABCD on one side and EFGH on the other
  Say ABCD went down
  Measure ABEF against CDSS (S = standard)
  If it balances
    Measure G and H, whichever goes up is lighter
  Else If ABEF goes down
         A or B is heavier, so measure A vs B
  Else if CDSS goes down
         C or D is heavier, so measure C vs D
  Similarly if EFGH went down

not sure it works if E|F was lighter? CDSS would go down, but C==D.

[FarmyardPants]

Agreed, I edited my post.