On a recent train journey I was drawn into a conversation by an elderly couple who were keen to tell me all about their grandchildren. Although proud of them all, their one complaint was the constant expense of buying birthday presents. There is at least one birthday amongst the grandchildren every calendar month, and April is particularly expensive for them because it sees the birthdays of three of the five pairs of twins. I remember them saying that they have exactly twice as many granddaughters as grandsons, but after they had left the train I realised that they hadnít told me how many grandchildren they have in total.