My youngest could read and write her name and basics too and do multiplication by 4 - with the logic...."Seven times five, Dad, thirty five and that's seven groups of five," being a response from behind my driving seat when testing her elder sister on multiplication. She was reading all the teacher's books for the kids with the phonetic stresses when she went to school to the staff's amazement - and then floored them with their first play. One kid couldn't make it at the last minute, so she stepped in and performed his role as well as hers, with one tiny stumble. The Headmistress got up at the end and in her closing remarks thanked her, pointing out that she not only knew the missing kid's part, she could have played any part...
However, I say I would be a little suspicious about a 3 year old writing to Sainsburys - or David Cameron. There's a Waitrose in Witney, not sure about Sainsbury's but I would think so....