Danny Baker's Sausage Sandwich Game

On Radio 5Live on a Saturday morning the Danny Baker Show features the Sausage Sandwich Game.  There are two contestants and a sporting celebrity involved.  Three questions are asked (unless there is a tie in which case additional questions are used to break the deadlock) and are the sorts of things that only the celebrity is likely to know.

The third question ("the question that gives the game its name") asks whether the celebrity would prefer to have on their sausage sandwich "red sauce, brown sauce, or no sauce at all".  Disappointingly there are no stats available for this, although Danny and Lynsey (his co-host) were incredibly surprised a few weeks ago when 'no sauce at all' was the winner.

This week (30 July 2016) Audley Harrison (Olympic boxing gold-medallist) was the guest.  The second question asked how many letters there were in the number of the house he lived in at the age of 10 or 12.  Danny then gave an example (so house number eight would have 5 letters, and house number thirteen would have 8 letters).  The contestants had to choose from: 3-6 letters, 7-9 letters, or more than that.

So: what do you choose?
My thoughts are below.



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Here are my thoughts:

It's complicated!

The first twelve numbers all fall into the first group (3-6 letters).
But then thereafter there are very few others that have only 3-6 letters.  Multiples of 10 up to and including ninety (but not seventy) are the only others that fit.  This means that after a strong start (12 out of 12) this turns into 13 out of 20, 14 out of 30 and 19 out of 100.
There won't be any after that ("one hundred" has 10 letters and even if you get as far as 10^100 then I I think you would say it as "a googol", which is 7 letters).

The 'teens' are then all 7-9 letters.  After that, for the 2-digit numbers up to 100 (but not in the seventies), the numbers ending in one, two and six are in 7-9, while the rest are 10-or-more.

Forty-four is the point at which 7-9 overtakes 3-6 letters.
10-or-more overtakes 3-6 at fifty-seven.
The lead changes between 7-9 and 10-or-more a couple of times, but from ninety-four onwards it is all 10-or-more.  (Everything after that is 10-or-more.)

So what do we choose?   Almost every road will have at least 12 houses in it.  But many roads have more than that.  Not many have over 100 though.

Knowing a bit about the background to the person might help.  Danny must have been fairly confident that Audley didn't live in a house with a name, and knowing that Audley grew up in London will presumably help to tell us that there are more likely to be higher numbers in the streets, but realistically not higher than a couple of hundred.  (In the USA they seem to skip numbers with abandon, so house numbers of 2505 are not uncommon - we don't do that in England.)

FWIW Audley grew up in house twenty-seven, which gave 11 letters.