Mr Bean was rather unhappy. It was the day he had to resit his maths exam. He had really made a mess of the first one - trying to answer questions on  Calculus ; not realising there was another paper on  Trigonometry that he could have done. This time he decided to try the  Algebra paper.

He went into the exam hall and took out his  Letts revision guide. "Just a little bit of time for some last minute cramming!" he thought to himself. 

"Please take your places," called the invigilator, "Don't forget to leave your coats and bags at the back of the room."

He sat down next to  Wallace . "Hello there," Wallace began, "Would you like a piece of Wensleydale  Cheese? It always takes my mind off my troubles."

Bean grumbled and shook his head. He took out his pens and pencils. He had brought along his brand new  calculator , just on the off chance that he could draw some pictures on it if he finished early.  Teddy had bought him a book about programming in Logo and he was very proud that he had actually succeeded in drawing three sides of a square. He wasn't quite sure how to get the fourth side to join up because they weren't all quite the same length but it wasn't too bad because the angles were nearly 90 degrees.

"You have 1 hour in which to complete the Algebra paper. You may begin."

Bean read the question carefully: "Add the following numbers together - 1 + 2 + 3 + 4 + ...... + 999 + 1000" He carefully got his pencil and ruler and set out the sum:

Next he switched his calculator on. He decided to use the fancy  statistics button with the  sigma sign on it. He entered each number very carefully and got the answer - 2009.

"Mmmm, " he thought, "That was pretty tricky!" He looked at the clock - still 45 minutes to go. He looked across to see what Wallace had done. There were quite a few xs and ys on his paper and some brackets and things. "Oh no," he thought, "Got it wrong again!"

Bean looked at the exam paper again. Why were there some dots in the middle of it? Could it be that he had to add all of the numbers in-between 4 and 999 as well? This is certainly what Wallace did.

The problem was set to a young boy called Carl  Gauss , back in the 18th century. He solved it very quickly. If you begin with adding the numbers from 1 to 5 first, then try numbers from 1 to 10, you should be able to see a pattern. Each time you find a total, you get a triangular number, so you need to find the general rule for triangular numbers, then substitute 1000 for x, and low and behold you will get the answer to Gauss, Wallace and Bean's problem - 500500.

Gauss went on to become one of the most famous mathematicians of all time, whereas Mr Bean didn't!

He got into his Mini and sadly drove away, bumping into a Robin Reliant on his way to the department store. He decided it was time for Teddy to buy him another present. Down in the basement, he found the toy department. There was a big display of Ferris Wheels and other  fairground toys made from something called  Knex ! He bought the biggest kit he could find and the book of ideas.

Yes! He'd devised a cunning plan - he would study hard with his new toy and take the Mechanics paper when he resat his maths exam next time!