Julian of Hethersett High School made a table of the days of the week on 1 January every year from the year 2000 to the year 2100. He used the fact that the day of the week 'moves on' by $1$ day each year (why is that?) apart from immediately after a leap year when it 'moves on' by $2$ days. The pattern repeats after $28$ years.
The first Saturday 1 st January after 2060 is in 2061 so Millennium Man will retire on his 61 st birthday. The 1st January falls on a Saturday four times every $28$ years. It falls on a Saturday $15$ times this century so his birthday will occur on a Saturday $15$ times during this century.
Well done also Lizzie and Hollie, The Mount School, York and Fiona, Stamford High School, Lincolnshire. Congratulations also to Katherine and Rosalind from Chawson First School Droitwich who told us:
We made a note of which years were leap years and then counted up all the Saturdays. The first question came out as 2061 and the second came out as $15$.