My source says that there are an infinite number of numbers, n, such that n+1 is a square and 2n+1 is also a square. The smallest is when n = 24. i.e. 24+1 = 25 = 5^2 and 2*24+1 = 49 = 7^2. The next four are 840, 28 560, 970 224, 32 959 080. [...]

What is the last digit of 777777333333?

Although I’ve only used 7’s and 3’s, you should be able to generalise the 777777 and 333333 to get the same result.

A farmer asked a worker to weigh 5 trusses of hay. The fool weighed them two at a time in all possible ways, and found that the weights were:

110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 units.

What are the weights of the individual trusses?

As the last one was easy, here’s another already.

A banana seller sells half his bananas plus half a banana on the first day. He does the same the next day, and the next day, and so on, until he finally runs out of bananas at the end of the tenth day. How many bananas did [...]

A man bought 6 barrels of booze. 5 contained wine and one contained beer. The sizes of the barrels were 15, 16, 18, 19, 20 and 31 gallons (luvvly jubbly). He sold a number of barrels of wine to one customer, and later sold some more barrels of wine to another customer. The second customer [...]

A deck of cards is split into 4 piles of 13. You take 1 card at a time from the top of any of the piles. Repeat until there are no cards left. How many different orders could you do that in?

If you crack that, then you should be able to generalise to piles of [...]

Seven gents A,B,C,D,E,F and G play a silly game. In order of their names, each doubles the amount of money that the others have in their pockets (from his own pocket). i.e. the money simply gets redistributed.

When all seven have taken their turn, each ends up with $128.

How much money did each of the gents [...]

This is like another old ToM. LOL and pretty easy.

If each of the “+”’s could be either “+” or “-” or “*” or “/” then

how many different answers could there be?

And what would be the largest and the smallest answers?

Here’s one I pinched from the old ToM site. In my opinion, the official answer was wrong and only one person got it right (for the right reason). I’ll post a link to the page after this has run it’s course.

Tom, Dick and Harry are in prison. One of them has been randomly selected to [...]