A race within a race

2009-03-04, , Comments

In 2003 the route of the Bristol half marathon took runners out of the city, following the Portway along the base of the Avon Gorge before turning 180° and taking them straight back again. So runners heading out along one side of the road got to watch the faster runners in front of them, heading back.

Nick Rose then Nick Rose now

The beauty of the Avon Gorge was probably lost on most competitors, myself included. What did impress me, though, was the sight of Nick Rose sprinting back along the Portway, his white hair swept back by his astonishing speed. Despite being 13 years older than me he completed the 13 mile race 13 minutes ahead of me. (I did beat Steve Cram though!)

The 2003 Bristol half marathon featured a race within a race, the “Legends Challenge”, which reunited veteran British athletes Nick Rose, Steve Cram, Tim Hutchings, Hugh Jones, Steve Jones and Mike McLeod to compete against each other for the first time since the 1984 Los Angeles Olympics. Nick Rose won this race within a race, aged 52, in 16th place overall, with a time of just 1:11:08. This inspiring result set me wondering about another slice of the results: starting with a list of runners ordered by their finishing time in a race, select, in order, a sublist of runners who are getting younger. What is the longest such sublist?

Unfortunately I don’t have access to the full results for the Bristol 2003 half marathon. Instead, here are the top 20 finishers in the 2008 New York marathon1.

  1. MARILSON GOMES DOS SANTOS, 31, M, 2:08:43
  2. ABDERRAHIM GOUMRI, 32, M, 2:09:07
  3. DANIEL RONO, 30, M, 2:11:22
  4. PAUL TERGAT, 39, M, 2:13:10
  6. ABDI ABDIRAHMAN, 31, M, 2:14:17
  7. JOSH ROHATINSKY, 26, M, 2:14:23
  8. JASON LEHMKUHLE, 31, M, 2:14:30
  9. HOSEA ROTICH, 29, M, 2:15:25
  10. BOLOTA ASMEROM, 30, M, 2:16:37
  11. LUKE HUMPHREY, 27, M, 2:18:38
  12. HENDRICK RAMAALA, 36, M, 2:19:11
  13. MOHAMMED AWOL, 30, M, 2:19:13
  14. KASSAHUN KABISO, 25, M, 2:19:54
  15. JACOB FREY, 27, M, 2:20:17
  16. GENNA TUFA, 24, M, 2:20:23
  17. KYLE SHACKLETON, 22, M, 2:20:38
  18. TEKLU TEFERA DENEKE, 29, M, 2:20:47
  19. BOAZ CHEBOIYWO, 30, M, 2:21:40
  20. DERESSE DENIBOBA, 26, M, 2:21:54

As you can see Paul Tergat, 39, finished ahead of the younger runner Abdi Abdirahman, 31, who beat Bolota Asmerom, 30, etc., giving a sublist of 7 runners which fits our criteria. Certainly this isn’t the only such sublist of this small sample, but is there a longer one?

After a few minutes we may convince ourselves we’ve found an optimal solution. How would you approach this problem for the full results list, ending with YURIKO OKADA, 59, F, 9:59:58 in 38096th place?

How many runners?

I’ll be discussing this problem in the next few posts, so please make sure you’re subscribed to read on. In the meanwhile, here’s a picture of the Avon Gorge taken from the western pier of the Clifton Suspension bridge. You can see the Portway down at the bottom. Nick Rose is a past winner of the Bristol Half Marathon. In 1979 he set a world record time for the distance of 1:02:36, and his personal best of 1:01:03 still stands as a British record. He lives in Bristol, now working at “Up and Running” in Westbury Park, and he continues to participate in the sport.

Avon Gorge and Clifton Suspension Bridge

1 I’m using capital letters since these names are scraped directly from the New York Marathon website, which uses capital letters almost exclusively, except for non-ascii athletes such as CORNé VAN OIRSCHOT.