Several suggested that, with energy-saving being an important factor, the one whose pseudopod was nearest the button would press it. But would they not have taken that into account when calculating where to sit and therefore be at identical distances?
Katy Kawkwell says that infinite intelligence is not energy efficient. Jeanette Solomons says their laziness outweighs their mental acuity. EM Solomons points out that an IIM may not be able to open a sardine tin. Graham Smith hopes they'll learn that intelligence gives the freedom to act irrationally.
Christine Jones says that an infinitely intelligent being should realise that if you want something done, you have to do it yourself.
GF Steele thinks it's a question of courtesy and communication, and Adam Sobey explains how Martians use personal identification numbers to decide randomly which will be first to make eye contact.
Brian W Aldiss says they were not Martians but imposters. "Martians of infinite intelligence do not travel on No 19 buses. Nor do they walk. They zyte."
Roger Davidge says that Phobos, the fat one, will not push first, because Deimos, with the quicker reaction time, will surely do so after Phobos has missed his chance.
Kevin Burdon says that any IIM travelling to Centre Point would take the Piccadilly line, changing at Leicester Square. Derek Newson points out that infinitely stupid Venusians also miss their stops. Duncan Bull and Navin Patel both blame Mrs Thatcher.
Julian Jacobs says this dilemma is the reason why two Martians never board the same 19 bus - and they know there's another close behind anyway.
Rufus Isaacs points out that the No 38 bus covers much the same route as the 19, and also, unlike the 19, is red, a Martian's favourite colour. Finally "any Martian of infinite intelligence will realise that, as 38 x 1 = 19 x 2, only one of them need make the journey, thus saving one fare and solving the whole problem. The prize, Mr Isaacs, is yours.