Enigma 190: Purely by coincidence
From New Scientist #1335, 9th December 1982 [link]
It took quite some time to drive my nephew Henry home last Saturday. There were a number of delays caused by road works and traffic jams but it didn’t seem to take so long because of the excellent programmes on the radio. Henry was quieter than usual so at the end of the journey I asked him: “Do you like classical music?”
“I wasn’t listening — I was multiplying the outer two digits of your 24-hour clock and noting when the result was equal to the product of the two inner digits.
“I should think that such coincidences occurred quite often,” I said.
“Not if one excludes products that are zero — and those formed by the same two digits such as at 12:12 when we started. The last coincidence was just before you switched off the ignition at 23:46.”
When did the other coincidences occur?