Sport climbing at the 2020 Summer Olympics – Women's combined
Sport climbing is a new event (one of four) at the 2020 Summer Olympics in Tokyo, and it just finished. Two events were held, one for men and one for women. The format consists of three disciplines: lead climbing, speed climbing and bouldering. The winner is determined based on who performs best in all three disciplines.
Let's look at the women's event. In the final round, each of eight competitors competed in each of the three disciplines. Each competitor received a rank, a distinct integer from 1 to 8, in each of the disciplines. (There were no ties in the individual disciplines.) The scores were multiplied and sorted; the lowest scores received medals.
The final scores of the women's final round of sport climbing at the 2020 summer Olympics were as follows:
- 🥇 Janja Garnbret: 5
- 🥈 Miho Nonaka: 45
- 🥉 Akiyo Noguchi: 64
- Aleksandra Mirosław: 64
- Brooke Raboutou: 84
- Anouck Jaubert: 84
- Jessica Pilz: 90
- Seo Chae-hyun: 112
As you can see, there were ties after multiplying the competitors' scores. Because these ties were both head-to-head (between two competitors), they were resolved by comparing the relative performance of the tied competitors in the three disciplines: whoever was better in more of the disciplines is ahead in the final order. (So, for example, we know that Brooke Raboutou performed better than Anouck Jaubert in more individual disciplines.)
Part one: Who were the winners of the three individual disciplines? (Of course, it's not possible to distinguish the disciplines from the information provided – how could you tell the difference between, eg, lead and bouldering? – but it's possible to say who the winners were.)
The speed discipline has a rather unusual format. The competitors are seeded from 1 to 8 based on an earlier round. Then, in a standard bracket pairing (1 vs 8, 2 vs 7, 3 vs 6, 4 vs 5), the competitors compete in pairs for who can climb a standardized speed wall faster. The winners proceed to a winners bracket, while the losers proceed to a losers bracket. Everyone continues to participate in two more speed climbs; for example, one of the pairs in the second part of the bracket is (the winner of 1 vs 8) vs (the winner of 4 vs 5). After three such climbs, the contestants end up "sorted" and receive a corresponding rank.
It's honestly very hard to describe this process in words. Here's a picture of the bracket used: As you can see in the image above, the seeds for the speed round were as follows: 1. Aleksandra Mirosław, 2. Anouck Jaubert, 3. Miho Nonaka, 4. Akiyo Noguchi, 5. Jessica Pilz, 6. Brooke Raboutou, 7. Janja Garnbret, 8. Seo Chae-hyun.
The resulting sorted order is: 1. Winner of Race 12, 2. Loser of Race 12, 3. Winner of Race 11, 4. Loser of Race 11, 5. Winner of Race 10, 6. Loser of Race 10, 7. Winner of Race 9, 8. Loser of Race 9. These ranks are the ones used in the multiplication of the final scores above.
Bouldering and lead use a more straightforward format, which I will not describe here because the information does not help reconstruct the results. For both the bouldering and lead disciplines, the competitors climb and end up with ranks from 1 to 8 in a relatively direct manner.
Necessary hint for the puzzle below: I personally find the lead discipline rather enjoyable to watch, as I enjoy lead climbing myself. It's nice that the winner of the lead discipline did so well overall, but I was sad that the 2nd and 3rd places in lead (who, presumably, would have won the silver and bronze medals had there been separate medals for lead climbing) ended up in the last two places (7th and 8th) of the combined ranking!
Part two: What were the full sorted orders of the competitors in all three disciplines?