### Tournament Brackets

For the three first Selective Science Fights, the Tournament Bracket established at the Opening Ceremony by drawing lots determines what Team competes in what Group and the sequence of performances in each Group. In contrast, the Brackets for Science Fight 4 and onwards depend on the Team Rank after the last completed Science Fight and no longer determine the sequence of performances within a Group, which is decided by winner of Captain's Contest.

The Tournament Bracket is established according to an exact procedure made public by the GC during the Opening Ceremony. Building such a Bracket is an interesting combinatorial optimization puzzle similar to the *Social Golfer Problem* with many additional constraints.

The exact structure of an IYNT Bracket aims at such a distribution of Teams among the Groups that the following criteria are respected, in order of decreasing priority:

**The number of parallel competition Groups is brought to an absolute minimum.**It therefore equals*N*/3, rounded up to the next whole number, where*N*is the total number of Teams in the IYNT. Consequently, there can be no more than 2 two-Team Groups during any Science Fight.**No two Teams meet more than once**prior to the Selective Science Fight 4. It is possible to fully satisfy this condition for*N*≥7 and*N*=4. Ensuring the minimum number of such repeated meetings per any Team is an absolute requirement for*N*=5 and*N*=6 when Teams are arranged such that no two of them meet more than twice.**Each Team plays as few two-Team Science Fights as possible**prior to the Selective Science Fight 4. For*N*≥16, each Team plays no more than one two-Team Science Fight. For*N*≥5, each Team plays no more than two two-Team Science Fights. In each such instance, the number of two-Team Science Fights per Team is distributed in the most even manner.- By passing from one Science Fight to next Science Fight,
**each Team switches their Role**in Stage I in the standard order (Reporter-Reviewer-Opponent.) This condition is fully satisfied for any*N*≥2, except*N*=5 and*N*=6 when all possible Roles are switched in a random order. - As to ensure that
**no two Teams from one country meet**prior to the Selective Science Fight 4, they would draw lots from a sufficiently large pool such that any combination of pairs in this pool never meets. This procedure is similar to*seeding*and requires pools no smaller than the number of Teams from one country. Such pools, of different size, exist for any*N*≥5. For convenience, the largest pools have the size of*N*/3 (rounded up) and are arranged such that all Teams playing a particular Role in Stage I of Science Fight 1 do not meet each other in any Science Fight. **No Team competes in any Group more than once.**This condition is enforced only when all higher-level priorities are achieved. It is then possible to fully satisfy the condition for*N*≥19. Ensuring the minimum number of and the most even distribution of returns to a Group is a lower-level priority for*N*<19. For*N*≥5, no Team ever plays in once Group more than twice.

Below are given exemplary Tournament Brackets of up to *N*=21 Teams, where the numbers indicate the lot.

### 19...21 Teams: 7 Groups

Group A | Group B | Group C | Group D | Group E | Group F | Group G |
---|---|---|---|---|---|---|

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

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

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

Each Team meets 6 other competitors, each of them exactly once.

In case of twenty Teams, Team 21 is omitted, and Teams 3, 5, 7, 9, 11, 14 land once in a two-Team Group. In case of nineteen Teams, Teams 20, 21 are omitted, and all Teams except 1, 12, 15, 16, 17, 18, 19 land once in a two-Team Group.

Each team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

All Teams play only once in one Group.

These pools of Teams never meet in whatever mutual pairing: 1+2+3+4+5+6+7 (Reporters in Stage I, SF 1), 8+9+10+11+12+13+14 (Opponents in Stage I, SF 1), 15+16+17+18+19+20+21 (Reviewers in Stage I, SF 1), 1+10+11+13+14, 1+16+18+20+21, 2+8+11+12+14, 2+15+17+19+21, 3+8+9+12+13, 3+15+16+18+20, 4+9+10+13+14, 4+16+17+19+21, 5+8+10+11+14, 5+15+17+18+20, 6+8+9+11+12, 6+16+18+19+21, 7+9+10+12+13, 7+15+17+19+20, 8+16+17+19+21, 9+15+17+18+20, 10+16+18+19+21, 11+15+17+19+20, 12+16+18+20+21, 13+15+17+19+21, 14+15+16+18+20 (21 fivesome pools.)

### 16...18 Teams: 6 Groups

Science Fight | Group A | Group B | Group C | Group D | Group E | Group F |
---|---|---|---|---|---|---|

1 | [1 7 13] | [2 8 14] | [3 9 15] | [4 10 16] | [5 11 17] | [6 12 18] |

2 | [8 18 4] | [9 13 5] | [10 14 6] | [11 15 1] | [12 16 2] | [7 17 3] |

3 | [13 3 11] | [14 4 12] | [15 5 7] | [16 6 8] | [17 1 9] | [18 2 10] |

Each Team meets 6 other competitors, each of them exactly once.

In case of seventeen Teams, Team 18 is omitted, and Teams 2, 4, 6, 8, 10, 12 land once in a two-Team Group. In case of sixteen Teams, Teams 17, 18 are omitted, and all Teams except 13, 14, 15, 16 land once in a two-Team Group.

Each team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

Teams 13, 14, 15, 16, 18 play twice in one Group, and all others play only once in one Group.

These pools of Teams never meet in whatever mutual pairing: 1+2+3+4+5+6 (Reporters in Stage I, SF 1), 7+8+9+10+11+12 (Opponents in Stage I, SF 1), 13+14+15+16+17+18 (Reviewers in Stage I, SF 1), 1+8+10+12, 1+14+16+18, 2+7+9+11, 2+13+15+17, 3+8+10+12, 3+14+16+18, 4+7+9+11, 4+13+15+17, 5+8+10+12, 5+14+16+18, 6+7+9+11, 6+13+15+17, 7+14+16+18, 8+13+15+17, 9+14+16+18, 10+13+15+17, 11+14+16+18, 12+13+15+17 (18 foursome pools.)

### 13...15 Teams: 5 Groups

Science Fight | Group A | Group B | Group C | Group D | Group E |
---|---|---|---|---|---|

1 | [1 6 11] | [2 7 12] | [3 8 13] | [4 9 14] | [5 10 15] |

2 | [7 15 3] | [8 11 4] | [9 12 5] | [10 13 1] | [6 14 2] |

3 | [11 3 10] | [12 4 6] | [13 5 7] | [14 1 8] | [15 2 9] |

Each Team meets 6 other competitors, each of them exactly once.

In case of fourteen Teams, Team 15 is omitted, and Teams 2, 3, 5, 7, 9, 10 land once in a two-Team Group. In case of thirteen Teams, Teams 14, 15 are omitted, Teams 2, 9 land in a two-Team Group twice, Teams 1, 3, 4, 5, 6, 7, 8, 10 land in a two-Team Group once, and Teams 11, 12 only land in three-Team Groups.

Teams 6, 7, 8, 9, 10 play once in one Group, all others play twice in one Group.

Each team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

These pools of Teams never meet in whatever mutual pairing: 1+2+3+4+5 (Reporters in Stage I, SF 1), 6+7+8+9+10 (Opponents in Stage I, SF 1), 11+12+13+14+15 (Reviewers in Stage I, SF 1), 1+7+9, 1+12+15, 2+8+10, 2+11+13, 3+6+9, 3+12+14, 4+7+10, 4+13+15, 5+6+8, 5+11+14, 6+13+15, 7+11+14, 8+12+15, 9+11+13, 10+12+14 (15 threesome pools.)

### 10...12 Teams: 4 Groups

Science Fight | Group A | Group B | Group C | Group D |
---|---|---|---|---|

1 | [1 5 9] | [2 6 10] | [3 7 11] | [4 8 12] |

2 | [8 10 3] | [5 11 4] | [6 12 1] | [7 9 2] |

3 | [10 4 7] | [11 1 8] | [12 2 5] | [9 3 6] |

Each Team meets 6 other competitors, each of them exactly once.

In case of eleven Teams, Team 12 is omitted, Teams 1, 2, 4, 5, 6, 8 land once in a two-Team Group, and Teams 3, 7, 9, 10, 11 always land in three-Team Groups. In case of ten Teams, Teams 11 and 12 are omitted, Teams 1, 4, 5, 8 land in two-Team Groups twice, Teams 2, 3, 6, 7 land in a two-Team Group once, and Team 10 always lands in three-Team Groups.

Teams 9, 10, 11, 12 play in one Group twice, all others once.

Each Team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

These pools of Teams never meet in whatever mutual pairing: 1+2+3+4 (Reporters in Stage I, SF 1), 5+6+7+8 (Opponents in Stage I, SF 1), 9+10+11+12 (Reviewers in Stage I, SF 1), 1+7, 1+10, 2+8, 2+11, 3+5, 3+12, 4+6, 4+9, 5+10, 6+11, 7+12, 8+9 (12 pairs.)

### 7...9 Teams: 3 Groups

Science Fight | Group A | Group B | Group C |
---|---|---|---|

1 | [1 4 7] | [2 5 8] | [3 6 9] |

2 | [4 8 3] | [5 9 1] | [6 7 2] |

3 | [7 3 5] | [8 1 6] | [9 2 4] |

Each Team meets 6 other competitors, each of them exactly once.

In case of eight Teams, Team 9 is omitted, and each Team lands once in a two-Team Group, except for Teams 7, 8 which always land in three-Team Groups. In case of seven Teams, Teams 8, 9 are omitted, and each Team lands twice in two-Team Groups, except for Team 7 which always lands in three-Team Groups.

Each Team plays in one Group exactly twice.

Each Team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

These pools of Teams never meet in whatever mutual pairing: 1+2+3 (Reporters in Stage I, SF 1), 4+5+6 (Opponents in Stage I, SF 1),
7+8+9 (Reviewers in Stage I, SF 1).

### 5...6 Teams: 2 Groups

Science Fight | Group A | Group B |
---|---|---|

1 | [1 3 5] | [2 4 6] |

2 | [3 6 4] | [5 2 1] |

3 | [6 1 2] | [4 5 3] |

Each Team meets 4 other competitors, two of them once and two of them twice.

In case of five Teams, Team 6 is omitted, Teams 2, 4 land in two-Team Groups twice, Teams 1, 3 land in a two-Team Group once, and Team 5 always lands in three-Team Groups. Teams 1, 2, 3, 4 then meet other 3 competitors, and Team 5 meets 4 other competitors.

Each Team assumes each of three Roles in Stage I of every Science Fight, changing them in random order.

Each team Plays in one Group exactly twice.

These pairs of Teams never meet: 1+4, 2+3, 5+6. These pairs or Teams meet once: 1+3, 1+6, 2+4, 2+5, 3+6, 4+5. These pairs of Teams meet twice: 1+2, 1+5, 2+6, 3+4, 3+5, 4+6.

### 4 Teams: 2 Groups

Science Fight | Group A | Group B |
---|---|---|

1 | [1 2] | [4 3] |

2 | [2 3] | [4 1] |

3 | [3 1] | [2 4] |

Each Team meets all 3 other competitors, each of them exactly once.

Each Team assumes each of two Roles in Stage I of Science Fights, changing them from Reporter to Reviewer-Opponent.

Each Team plays in one group two (1, 2, 3) or three (4) times.

### 2...3 Teams: 1 Group

Science Fight | Group A |
---|---|

1 | [1 2 3] |

2 | [2 3 1] |

3 | [3 1 2] |

Each Team meets all 2 other competitors, each of them exactly three times.

In case of two Teams, Team 3 is omitted, and Teams 1, 2 land in a two-Team Group three times.

Each Team assumes each of three Roles in Stage I of every Science Fight, changing them from Reporter, to Reviewer, and to Opponent.

Each Team plays in one group three times.

### 16 Teams (IYNT 2013)

SF | Group A | Group B | Group C | Group D | Group E | Group F |
---|---|---|---|---|---|---|

1 | [1 7 13] | [2 8 14] | [3 9 15] | [4 10 16] | [5 11 | [6 12 |

2 | [12 | [7 | [8 13 6] | [9 14 1] | [10 15 2] | [11 16 3] |

3 | [15 6 11] | [16 1 12] | [ | [ | [13 4 9] | [14 5 10] |

4 | [2-9- [2 9 | [3-10-13] [10 3 13] | [4-11-14] [11 4 14] | [5-12-15] [5 12 15] | [6-7-16] [7 6 16] | [1-8- [1 8 |

sF | [r1-r6-r7] [12 2 9] | [r2-r5-r8] [7 6 3] | [r3-r4-r9-rg] [5 1 4 10] | --- | --- | --- |

Fin | [vA-vB-vC-vt] [10 11 7 3] | --- | --- | --- | --- | --- |

As to ensure that any two Teams from one country never meet until Semi-Finals, two Teams of Bulgaria, three Teams of Russia, and Team of Moldova drew lots from the pool 1+2+3+4+5+6. Next, three Teams of Turkey, and Teams of Afghanistan, Belarus, and Georgia drew lots from the pool 7+8+9+10+11+12. The rest drew lots from the pool 13+14+15+16. The bracket was fixed in the Regulations. Despite restrictions of the competition building to accommodate all three-Team Groups, the bracket was not amended, but the Group labels were switched on the doors for two-Team Groups.

### 5 Teams (IYNT 2014)

Science Fight | A | B |
---|---|---|

Science Fight 1 | [1 3 | [2 6 4] |

Science Fight 2 | [4 6 1] | [ |

Science Fight 3 | [ | [6 2 3] |

Science Fight 4 | [1 6 3] | [2 |

Finals | [r1-r2-r3] [4 6 2] | --- |

As to ensure that two Teams of Bulgaria never meet before Finals, they drew lots from the pool 1+2. The rest drew lots from the pool 3+4+5+6, because a sixth Team was expected to arrive just after the Opening Ceremony, but never appeared.

### 10 Teams (IYNT 2015)

SF | Group A | Group B | Group C | Group D |
---|---|---|---|---|

1 | [1 3 7] | [4 8 x] | [2 5 9] | [6 10 x] |

2 | [9 6 x] | [10 3 2] | [7 4 x] | [8 5 1] |

3 | [5 10 x] | [6 2 7] | [3 8 x] | [4 1 9] |

4 | [R1+R8+R9] [6 3 4] | [R3+R6+x] [2 5 x] | [R2+R7+R10] [8 7 1] | [R4+R5+x] [9 10 x] |

sF | [R5+R4+R1] [3 10 5] | [R6+R3+R2] [8 7 9] | --- | --- |

Fin | [vA+vB+v1] [9 5 3] | --- | --- | --- |

The bracket was custom-designed for the IYNT 2015. Countries represented by one Team drew lots from the pool 3+4+5+6+7+8+9+10 (Belarus-Spectrum pulled 10, China 3, Bulgaria 6, Croatia 5, and Georgia-Georgians 9), thus leaving lots 4, 7, 8 in the pool. As to ensure that three Teams from Russia never meet until Semi-Finals, Russia-MG 12 and Russia-Voronezh-1 drew lots from the pool 1+2, and then Russia-Voronezh-2 drew lots from an intersection of sets 4+6+8+10 and 4+7+8 (lots remaining from the first pool; Russia-MG 12 pulled 1, Russia-Voronezh-1 pulled 2), eventually drawing 4 (from a choice of 4 and 8.) Serbia-1 and Serbia-2 were then left with choices also not meeting until Semi-Finals (7 and 8), and pulled 8 (Serbia-1) and 7 (Serbia-2).

### 16 Teams (IYNT 2016)

SF | Group A | Group B | Group C | Group D | Group E | Group F |
---|---|---|---|---|---|---|

1 | [1 7 13] | [2 8 14] | [3 9 15] | [4 10 16] | [5 11 | [6 12 |

2 | [9 16 6] | [12 13 3] | [7 14 4] | [8 15 5] | [10 | [11 |

3 | ||||||

3 | [r1 r6 r7] [1 13 6] | [r2 r5 r8] [5 9 8] | [r3 r4 r9] [3 12 15] | --- | --- | --- |

4 | [r1+r12+r13] [15 8 1] | [r2+r11+r14] [14 5 7] | [r3+r10+r15] [10 11 3] | [r4+r9+r16] [13 4 16] | [r5+r8+ [9 12 | [r6+r7+ [6 2 |

sF | [r1+r6+r7] [5 4 12] | [r2+r5+r8] [2 1 9] | [r3+r4+r9] [6 3 10] | --- | --- | --- |

Fin | [vA+vB+vC] [3 5 1] | --- | --- | --- | --- | --- |

A bracket for 18 Teams provided in previous Regulations v. 2015/02/25 was amended for SF 2, SF 3, and SF 4 such that two-Team groups would always land in E and F, due to restrictions of the competition building. The initial bracket for SF 3 was not executed as only 9 Teams were allowed. Countries represented by one Team drew lots from the pool 1+2+3+4+5+6 (Belarus-Pahonia pulled 3, Croatia 5, Georgia-Georgians 1, and Russia-Voronezh 6). Three out of four Teams not meeting an age limit drew lots from the pool 13+14+15+16 (Iran-Black Intelligence pulled 13, Iran-Velayat 16, and Iran-Amordad 15). The lots remaining in both pools (2+4+14) were merged with the bulk of lots (7+8+9+10+11+12), and other teams drew lots from such a pool of 9 lots.