There's a clever formula that tells you which day of the week any date falls on. With practice you can do birthdays in your head.
The trick (rough)
Take the year's last two digits, divide by 4 (drop remainder), add the day, add a code for the month, add a code for the century. Mod 7. Map 0=Sunday, 1=Monday, …
John Conway's 'Doomsday rule' is a faster version. Skilled practitioners can do any date in under 2 seconds — purely in their head.