Review/improve anti collision circuit using hall effect sensors
A few comments as I scan through the schematic: 


Use ground symbols. These are instantly recognisable and avoids having to trace wires and would eliminate about 30% of them. 
Put V+ at the top. Put the socket at the right. 
What's a turn-on relay? If it's a transistor then show that in the symbol.


It's not clear why you added R1 to the circuit. It dilutes the changes as R6, 7, 8 and 9 are switched. 

The following table shows calculations show the percentage of V+ (10 V in your case, I think) at the junction of R6, 7, 8 and 9 for the various combinations.

                    5k + 39k pull-up      10k pull-up
1 x 10k -&gt; 10k           18%                  50%
2 x 10k -&gt;  5k           10.4%                33%
3 x 10k -&gt;  3k3           7%                  25%
4 x 10k -&gt;  2k5           5.4%                20%


You can see that decreasing R2 to 10k and shorting out R1 will result in much higher differences.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A cleaner solution?


If the sensors are analog then simplify the comparitor circuit as shown here. Most have open-collector outputs that can be paralleled in an 'OR' configuration.
If the sensors are digital then just wire the sensors in 'OR' configuration. Use diodes if required to prevent them fighting to pull high / low simultaneously.