You have 3 suitcases.  One of them weighs 37kg, one weighs 29kg, and the third, your carry-on bag, weighs 16kg.

The airline will not accept any bags over 32kg.  Any bags over 23kg carry a charge of £120.  Carry on luggage cannot weigh more than 12kg.

Calculate the most cost-effective weight distribution algorithm possible, whilst using a pair of electronic scales that will switch off after an hour, and which are also being used by dozens of other people solving the same problem.  You have 3 hours before your flight boards.

OK, I’m an English teacher (or at least I will be tomorrow), not a maths teacher.  Moving abroad for a year necessitates taking a lot of stuff – pretty much your entire wardrobe, plus electronic devices and equipment, plus of course your Russian learning and English teaching resources.  Coats, jacket and shoes alone will fill up one suitcase.  And suitcases weigh about 5kg to start with.

I played Airport Tetris for a good couple of hours, accepting I wouldn’t be able to carry on my carry on case, but thinking I could get at least 2 suitcases under 23kg.  My carry on problem was alleviated by my having placed a suitable shoulder bag in the biggest suitcase, which when removed (with its contents), brought the larger case to within striking distance of 23kg.  Perhaps, with a nice leisurely afternoon, and a pair of scales all to myself I could have got all three suitcases under 23kg and my carry on bag under 12kg.  However even then I would have had to pay a luggage excess for 2 extra check-in items.  My final score was 29kg, 27kg, 18kg (the luggage formerly known as carry on) and 10kg for my heroic shoulder bag, which as an added bonus fit snugly into the dimension check frame.  Once I gave up on getting either large case under 23kg, I was able to throw in scarves, cardigans, sweaters, hats, things I would have been forced to either wear onto the plane like an Arctic explorer, or leave at the airport.  The charges I had to pay – 2 overweight excess bags, at £120 a pop, £240.  Almost but not quite as much as my flight ticket!  Painful, but my hands were tied.

I’m now sitting the other side of security, just realising that the snow boots I’m wearing, while large, probably weigh less than my work shoes, and can also be filled with other items to take up minimal space.  Hindsight is a wonderful thing.