Councillor Claire Darke came up with the idea to help raise funds for good causes across the city.
The quiz will be held tomorrow after coronavirus restrictions prevented it from being held in the mayor's parlour.
But it means people will be able to take part from the comfort of their own home – with everyone urged to join in.
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Councillor Darke said: "I wish everyone a Happy New Year. I wish to thank all those who have supported the Mayoral Charities.
"2020 was a tough year, and it will continue to be so for many in 2021, but the people of Wolverhampton have been very supportive of one another so far and we much continue to care for another and stay safe and keep others safe.
"I hope this fun quiz can help you enjoy the new year just a little more, at least for an hour or two. Enjoy, be safe and I look forward to seeing you in 2021 at some point of joy and celebration."
The mayor hopes to tap into the quiz craze which has established itself through lockdown – and aims to raise some money for her chosen charities, by asking people to leave a small donation.
To donate, text the word wvmayor followed by a space, followed by the amount of your donation in whole pounds from one to 20 to 70085. So to donate £5, text "wvmayor 5".
Your message will cost the amount you choose to donate plus one standard message charge.
The quiz will be hosted on Wolverhampton Today on Facebook and the Mayor of Wolverhampton's Facebook page – and can be viewed in tomorrow's copy of the Express & Star.