Teaser 2964: “Bingo a go-go” lingo a no-go

From The Sunday Times, 14th July 2019 [link]

My rest home’s Bingo set uses numbers 1 to 99. To win, nine numbers on your game card must be called. Our caller, not knowing “bingo-lingo”, says “Number 1, total factors 1”, “Number 11, total factors 2” and “Number 30, total factors 8”, etc.

Yesterday, in one game, my hearing aid howled whenever a call started. I missed each number, but heard each “total factors” value. Fortunately, after just nine calls I shouted “HOUSE!” certain that I’d won.

I told my daughter how many different “factor” values I’d heard, but didn’t say what any of the values were. Knowing that I had won after nine calls, she could then be sure about some (fewer than nine) of my winning numbers.

Find, in ascending order, the numbers that she could be sure about.

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