Our local church runs a lottery which is a simpler version of the UK’s National Lottery. To enter, you have to pay 10 pence and on a card tick a certain number of boxes from those labelled 1,2,3, ... up to some number.
I am quite a gambler so I enter lots of times each week: In fact, I enter every possible combination in which no two of the chosen numbers are consecutive.
The lottery has been such a succes that the church wants to increase the number of possible combinations without having to reprint its lottery cards. So it has simply changed the rules so that from next week onwards entrants will have to tick one more number than they did previously. If I continue my system of entering every possible combination in which no two numbers are consecutive, then my weekly outlay will go up by 50%.
How many numbers are on the card?
From next week, how many boxes have to be ticked?