Leaping Years

Martin would only have birthday in a leap year. Contrary to general assumption that if the year number is divisible by 4 then it is a leap year, a leap year is defined as:

If the year number is divisible by 4 but not divisible by 100, then it is a leap year. But if the year number is divisible by 4 and 100 and also divisible by 400, then it is a leap year.

This means that 1900 was not a leap year but 2000 was. Then Martin had birthday in 1896, 1904. 1908, 1912....

• Martin was $4\times 365 + 1 = 1461$ days old on his 1896's birthday and it was on a ( $1461 \text{ mod }7 = -2$ ) Saturday (0 means Monday).
• He was $1461 + 8\times 365+1 = 4382$ days old on his 1904's birthday and it was on a ( $4382 \text{ mod }7 = 0$ ) Monday .

So he was $1904-1892= \boxed{12}$ years old when his birthday next fell on a Monday.