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If you’ve ever envied folks absorbed in puzzle magazines as you sit shuffling board papers on the train, here’s your chance to join in the fun with Lombard’s inaugural governance teaser:

Problem: Sir Andrew Witty and Sam Walsh are chief executives. Sir Andrew is 51. He started eight years ago. Shares in his company, GSK, are higher but have lagged behind the pharma industry by 64 per cent. Sam is 66. He started three years ago. Shares in his company, Rio Tinto are lower but by less than the mining sector.

Sir Andrew will retire in one year and has no nominated successor. Sam will retire in three months in favour of Jean-Sébastien Jacques. Jean-Sébastien knows a lot about copper mining. He is French, a fashionable nationality for FTSE 100 bosses.

Sam collects milk jugs. Sir Andrew collects money. He got £6.6m last year.

Everyone loves Sam, a grandfatherly Aussie. Sir Andrew is charismatic, and, inevitably, witty. But not everyone loves him. His non-fans include China, a country with 1.4bn inhabitants. In 2014, China fined GSK almost $500m for bribing doctors.

Neil Woodford, a powerful fund manager, has said for some time that Sir Andrew should do something else. Perhaps he could collect milk jugs too? Sam could show him the ropes. Perhaps GSK could sell its consumer division for £17bn to a company that knows about that sort of thing?

Question: On a scale of one to 10, how well have GSK and Rio handled their succession?

Answer: Rio Tinto gets eight. This is how it is supposed to happen. The transition is short, which makes it less destabilising. The successor looks credible. He comes from inside Rio, but isn’t a lifer. So he should bring fresh perspectives to the job. At 44 he’s much younger than Sam, so won’t be exposed to speculation about how much longer he’s got.

Sam stabilised Rio during the commodities crash. Jean-Sébastien has a chance to expand judiciously at a time when asset prices are low.

GSK gets a score of five. Sir Andrew’s retirement deadline is too long. It suggests foot-dragging in the face of shareholder pressure. He has no named successor. This might create a power vacuum. The succession process has become semi-public. Candidates such as finance director Simon Dingemans are more likely to feel embarrassed and leave if they don’t get the job.

GSK can improve its score by anointing a successor swiftly and trimming Sir Andrew’s tenure. Otherwise, his leave taking threatens to be as extended as that of a Wagnerian tenor who says he’s dying, then lies on stage like a beached whale for three hours singing about it.

jonathan.guthrie@ft.com