The double rainbow that Nathan and Zhang Mei see from the train when they arrive in England is wrongly generated. The secondary rainbow should be inverted with purple on the outside of the arc but in the movie red is on the outside. The rainbow should also be opposite the sun so the shadows on the ground should point towards it.
The UK team attend a training camp in Taipei. Training camps actually occur in the UK, usually at Trinity College, Cambridge.
The announcer at the IMO says "Welcome to the 59th IMO". This will in fact take place in 2018.
Immediately before the Olympiad begins, a team is huddled together and shout in unison, "Aussie aussie aussie, oi, oi, oi!" A familiar cry for Australians especially at sporting events, the group disbands and they are actually New Zealanders not Australians (Aussies). They wear the "All Blacks" of New Zealand colour and have Kiwi motifs on their shirts.
The IMO has never been held in Cambridge, England as the film suggests.
Luke disparages the decimal system on the grounds that it's only used because humans have ten digits on their hands. However, he then cites arbitrary reasons for base twelve such as 12 hours a night, 12 hours a day, 12 months for the Earth to orbit the sun - for not only are these also human constructs, the month is a crude approximation of the cycle of lunar phases which actually repeats 12.37 times per year.
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