combinatorics - Weekly group assignment algorithm with odd number of participants -

there round-robin solution question i asked before. works great number of people none of suggestions seem work once implement algorithm , try them out. i've tried many variations , (grouping last 1 whole bunch of other people, second group last group, different combinations, 2 , 4 last of bottom row, thought give me optimal solution still many duplicates). can suggest way go, or proof there cannot solution without 2 people working more once can stop trying make work. if want algorithm in java can post can play it.

thanks.

14 weeks 23 students in groups of 2 , 1 3 sufficiently undemanding local search able find solution.

 18  1 11|  3  4|  5  7|  9  6|  0 17|  2 12| 10 19| 15 16| 21  8| 14 20| 13 22|   6 13 18| 17  4|  5  0| 20  1| 12 11| 10  9|  2 14| 15  7|  3  8| 19 16| 21 22|  21 17  7| 19 22|  3  1|  2  8|  0 10| 14 12| 13 11|  6 16|  5 15| 18 20|  9  4|   8  1 13| 18  2|  6 11| 20  0| 12 10| 14 15|  5 17|  9 21|  4 19|  3 22| 16  7|   0  4 16| 17 20| 21  3|  7 18| 13 19|  1  5|  9 11| 15  2| 14  8| 10  6| 12 22|  12  1 17| 15  4|  8  6| 16 18|  9  0| 11 22|  5 14|  3  2|  7 13| 19 20| 21 10|   4  1 22| 12  8| 15  6|  7  0|  9 17| 11  3| 13  2|  5 18| 10 14| 19 21| 20 16|   0  1  6| 13 21| 15 12| 17  8| 20 10| 11  4|  3 14|  5 16|  7  2| 19  9| 18 22|  13 16  3|  2  9| 11 20|  6 17| 22 10|  5 12|  0 14| 15  1|  8 18| 19  7| 21  4|  14  1  7|  2  4|  5  9|  3  6|  8 10| 13 12| 21  0| 17 16| 22 20| 19 18| 11 15|  14 18 21| 12  4|  5  6|  2 19|  8 20|  1  9| 13  0| 11 16| 17 15|  3 10|  7 22|  21  6  2|  3 20|  5 13| 16  8| 18 17|  0 12| 22 14| 10  1|  9 15|  7  4| 11 19|   0 11  2|  6  4| 16 14|  7  8| 17 10|  1 19| 13  9|  3 18| 21 12| 20  5| 15 22|   1 16  2| 14 13|  3  7|  8  4| 11 10|  9 12|  0 18| 15 19| 17 22|  6 20| 21  5| 

here's java code made it.

public class schedule {   private final int weekcount;   private final int groupcount;   private final int personcount;   private final int groupfirstslot[];   private final int weekslotperson[][];    public schedule(int weekcount, int groupcount, int personcount) {     this.weekcount = weekcount;     this.groupcount = groupcount;     this.personcount = personcount;     int remainingpersoncount = personcount;     this.groupfirstslot = new int[groupcount + 1];     (int remaininggroupcount = groupcount;          remaininggroupcount > 0;          remaininggroupcount--) {       groupfirstslot[remaininggroupcount] = remainingpersoncount;       remainingpersoncount -= remainingpersoncount / remaininggroupcount;     }     this.weekslotperson = new int[weekcount][personcount];     (int week = 0; week < weekcount; week++) {       (int person = 0; person < personcount; person++) {         weekslotperson[week][person] = person;       }     }   }    public int getweekcount() {     return weekcount;   }    public int getgroupcount() {     return groupcount;   }    public int getpersoncount() {     return personcount;   }    public int getgroupfirstslot(int group) {     return groupfirstslot[group];   }    public int getweekslotperson(int week, int slot) {     return weekslotperson[week][slot];   }    public void swapweekslotperson(int week, int slotone, int slottwo) {     int temp = weekslotperson[week][slotone];     weekslotperson[week][slotone] = weekslotperson[week][slottwo];     weekslotperson[week][slottwo] = temp;   }    public int getconflictcount() {     int paircount[][] = new int[personcount][personcount];     (int week = 0; week < weekcount; week++) {       (int group = 0; group < groupcount; group++) {         (int slotone = groupfirstslot[group];              slotone < groupfirstslot[group + 1];              slotone++) {           int personone = weekslotperson[week][slotone];           (int slottwo = groupfirstslot[group];                slottwo < groupfirstslot[group + 1];                slottwo++) {             int persontwo = weekslotperson[week][slottwo];             paircount[personone][persontwo]++;           }         }       }     }     int conflictcount = 0;     (int personone = 0; personone < personcount; personone++) {       (int persontwo = personone + 1;            persontwo < personcount;            persontwo++) {         int pc = paircount[personone][persontwo];         conflictcount += pc * (pc - 1) / 2;       }     }     return conflictcount;   }    public static void main(string[] args) {     schedule sched = new schedule(14, 11, 23);     java.util.random rand = new java.util.random();     int oldcc = sched.getconflictcount();     while (oldcc > 0) {       int week = rand.nextint(sched.getweekcount());       int slotone = rand.nextint(sched.getpersoncount());       int slottwo = rand.nextint(sched.getpersoncount());       sched.swapweekslotperson(week, slotone, slottwo);       int newcc = sched.getconflictcount();       if (newcc < oldcc) {         oldcc = newcc;       } else {         sched.swapweekslotperson(week, slotone, slottwo);       }     }     (int week = 0; week < sched.getweekcount(); week++) {       (int group = 0; group < sched.getgroupcount(); group++) {         (int slot = sched.getgroupfirstslot(group);              slot < sched.getgroupfirstslot(group + 1);              slot++) {           system.out.printf("%3d",                             sched.getweekslotperson(week, slot));         }         system.out.print('|');       }       system.out.println();     }   } }