Singapore's Proposals for the IMOs
Singapore proposed two problems for the 1988 IMO:
SIN1. In a group n people, each one knows exaclty three others. They are seated around a table. We say that the seating is perfect if everyone knows the two sitting by their sides. Show that, if there is a perfect seating S for the group, then there is always another perfect seating which cannot be obtained from S by rotation or reflection.
SIN2. Let Q be the centre of the inscribed circle of a triangle ABC. Prove that for any point P,
a(PA²)+b(PB²)
+c(PC²)=
a(QA²)+b(QB²)
+c(QC²)+a+b+c(PQ²)
where a = BC, b = CA, c = AB.
SIN2 was shortlisted for the consideration of the Jury.
List of the Singaporean IMO representatives
| Year | Venue | Participants |
|---|---|---|
| 1988 | Canberra | Chan Hock Peng
Lim Jing Yee Ngan Ngiap Teng Cheong Kok Wui Yeoh Yong Yeow Tang Hsiu Khuen |
| 1989 | Brunswick | Lam Vui Chiap
Lee Mun Yew Ng Lup Keen Er Chiang Kai Yeoh Yong Yeow Tang Hsiu Khuen |
| 1990 | Beijing | Hsi Han Yin
Lim Li Woon Tan Chong Hui Lim Chu Wee Er Chiang Kai Chin Chee Whye |
| 1991 | Sigtuna | Chua Chek Beng
Pang Ki Khoon Tan Chong Hui Lim Chu Wee Ng Chee We Lim Li Ying |
| 1992 | Moscow | Chua Chek Beng
Ben Leong Wing Lup Pang Siu Taur Lim Chu Wee Ng Chee We Andrew Teng Huei Chong |
| 1993 | Istanbul | Chong Chan Vee
Tan Choon Siang Pang Siu Taur Tan Swee Heng Andrew Ng Yan Tak Wee Hoe Teck |
| 1994 | Hong Kong | Davin Chor Han Ping
Tan Choon Siang Pang Siu Taur Tan Swee Heng Tracey Ho Cui Ping Wee Hoe Teck |
| 1995 | Toronto | Davin Chor Han Ping
Koh Yi-Huak Tay Wee Peng Senkodan Thevandran Jeffrey Pang Wee Hoe Teck |
| 1996 | Bombay | Jordan Low
Daniel Tan Senkodan Thevandran Jeffrey Pang |