What a dumb exercise.
How do you present an idea that's as controversial as possible without making yourself look like a complete jackass (especially as it's such a ridiculous made-up problem that, even if it were a real situation, would simply never be addressed in this way)? It's an exercise that is very highly biased against sober, realistic, cynical, experienced individuals who are able to think up creative yet realistic solutions to real life problems. Instead, it favours domineering airhead types who have the gift of the gab and an ability to force their opinions on others, and who can dupe HR into thinking they're good all-rounders when in fact their only real strength is that they happen to be extroverts.
Also, the problem with team exercises is that your own rating depends on how the team as a whole does (despite what the assessors might say... it's called "associative theory" or something like that).. Which isn't very fair if you end up lumbered with a load of jackasses.
I think I should go for a career in HR. I'd have all sorts of good ideas for hoops to make candidates jump through. I think my first one would be to get them to write a song about the company in 45 minutes, emphasising our competitive advangage and their ideas for how they could solve global warming, then sing it to the group. There would be three judges (all from HR) and we would give them feedback Simon Cowell style before making our decisions as to whether they're through to the next round.