You had to be quite careful with this problem - Alice explained how she went about solving it:
First I got 24 lollipop sticks then I fiddled around and sorted out Jack's birthdays and put in Kate's birthdays where they fitted. I had 3 tries to get it right.
Alice sent in this very clear picture of the answer:
Amy and Nathan from Maadi British International School in Cairo also explained their reasoning:
We worked out it couldn`t be Jack's 7th birthday because that was too big. It couldn't be 5 because 5 was too small so it had to be 6 because it was in between the 5 and the 7. We had three more candles left so Kate had to be 2 years old. Kate was 1 when Jack was 4, so when Kate was 0, Kate was born and Jack had to be 3 years old.
Thank you to all of you for your very clear solutions.