How many recorded beatles songs were written by someone else?

Quite a few; The Beatles had a "rule" that singles wouldn't appear on LPs (albums) - although the rule was broken from time to time. The list of non-LP tracks are:

From Me to You

Thank You Girl

She Loves You

I'll Get You

I Want to Hold your Hand

This Boy

Komm, Gib Mir Deine Hand (a German language version of I want to hold your hand)

Sie Liebt Dich (German language She Loves You)

Long Tall Sally

Slow Down

Matchbox

I Call Your Name

I Feel Fine

She's a Woman

Bad Boy

Yes It Is

I'm Down

Day Tripper

We Can Work It Out

Paperback Writer

Rain

Lady Madonna

The Inner Light

Hey Jude

Revolution

Old Brown Shoe

You Know My Name

There were also a few "single only" versions of LP tracks (Love me do and Let it be have different versions for the single).

Many of these tracks have appeared on compilation albums and all the "missing tracks" appeared on the Past Masters CDs.