Originally posted by hypothetical
Could you put one coin from one bag, two coins from a second bag three coins from a third bag, and so on (all at the same time)? how many ever tenths of a gram it is over a full gram is the bag that had the 1.1 gram coins. Am i correct in my assumption?
yes they are.
and for the advanced problem: i've expressed it as a flowchartish
1: ballence1 sidea 4 against sideb 4
2: if 1 yeilded a ballence goto 17
3: mark which coins were on the high side and which were on the low side and which were unweighed in 1 as h, l, and b (for blank) respectivly
4: ballence2 sidea 3b and l against sideb 3l and h
5: if 4 yeilded a ballence goto 14
6: mark which coins were low, high, and unballenced in 4 as i, m, and c respectivly in addition to their previous markings
7: if 4 yeilded sidea high goto 11
8: ballence3 sidea hi against sideb bc
9: if 8 yeilded a ballence then lm is conterfit and goto end
10: hi is conterfit and goto end
11: ballence3 sidea lm against sideb lm
12: if 11 yeilded a ballence then the lm which was not ballenced in 11 is conterfit and goto end
13: the lm which weighed low in 11 is counterfit and goto end
14: ballance3 sidea h against sideb h
15: if 14 yeilded a ballence then the h which was not ballenced in 14 is counterfit and goto end
16: the h which weighed high in 14 is conterfit and goto end
17: mark the coins which were ballenced and not ballenced in 1 as d and u respectivly
18: ballence2 sidea 3d agianst sideb 3u
19: if 18 yeilded a ballence then the u which was unballenced in 18 is counterfit and goto end
20: change the marking on the u which was unballenced in 18 to a d
21: ballence3 sidea u against sideb u
22: if 21 yeilded a ballence then the u which was unballenced in 21 is counterfit and goto end
23: if 18 yeilded sideb high then the u which weighed high in 21 is counterfit and goto end
24: if 18 yeilded sideb low then the u which weighed low in 21 is counterfit
end
in retrospect there must have been a better way of expressing that.
i'm pretty sure it's airtight, but it dont have any more paintence with which to check.