A prototrophic Hfr strain of E. coli with the genotype trp+ purB- pyrC+ is conjugated with an F- strain with the genotype trp- purB+ pyrC- . The trp gene is known to enter last. The following numbers of recombinants were isolated:
trp+ purB- pyrC- 
trp+ purB+ pyrC+ 
trp+ purB+ pyrC- 
trp+ purB- pyrC+ 
Draw a genetic map that shows the order in which these genes are arranged and the distances between them.
I started off by making these assumptions:
trp+ purB- pyrC- 0 (the lowest #, must be double recombinant(DC)
trp+ purB+ pyrC+ (must be single recombinant(SC)
trp+ purB+ pyrC- (must be single recombinant(SC)
trp+ purB- pyrC+ (the highest #, must be parental(P)
Now since i know which one is DC and which one is P I can find the middle gene:
trp+ purB- pyrC+ (224)- P
trp+ purB- pyrC- (0)- DC
The only gene that varies is pyrC thus PyrC is the middle gene.
Consequently, the distance from trp-->PyrC=(DC+SC)/400=(0+44)/400= 0.11 or in map units it becomes 11
similarly, the distance from pyrC->pur B=(0+132)/400=0.33 or 33 m.u.
and here's the part im confused about: I only have 1 parental and i cant make the cross to figure out which is trp-->PyrC and which is pyrC->pur B. Even though i'm confident i got the right numbers how do i figure which one is 11 and which one is 33???
ps: I know it's a silly question after solving 99% of the problem it just that im used to do mapping with 2 parentals that i get lost when there is only 1 parental.
I actually figured it out, its not a regular genetic mapping problem but the bacterial genetic mapping(in particularly High resolution mapping). Thus, all the steps above are correct and answering my own question the way to figure out which direction it goes is just to compare the parentals given:
trp+ purB- pyrC+
trp- purB+ pyrC-
(NOTE: ignore the trp minus since we solve for it)
doing the crossovers will yield the same results listed above,its just that it's more precise way to know which one is trip --->pyrC and which one is pyrC--->purB
PPS:SMC Bio 22 students doing problem set 1 in the future, you can thank me later.