Woody Allen famously dismissed it as his “second favourite organ” but the brain is increasingly recognised as a muscle that benefits from regular exercise. According to neuroscientists, the term “use it or lose it” is never truer than for cognitive abilities.

The science behind some of the more outlandish claims for computer games that are supposed to improve your cognitive powers, is a matter of debate. However, you don’t need to pay £20 to give a game a try. The internet features a host of websites that can stretch your imagination and improve your mental prowess in a range of skills. Some are expensive rip-offs, but many are free, as our guide to the best of them shows.

GENERAL TRAINING

Begin by downloading the Brain Fitness 101 e-guide by Sharp Brains, available free at tinyurl.com/6nlz9j. The guide gives a good overview of how mental exercises keep the brain on top form.

For a rigorous look at how well brain training works, read the recent New Scientist cover story, “Is it worth going to the mind gym?”, available free at tinyurl.com/6s9odg.

The best-known example of computer-game mental exercise is Nintendo’s Brain Training series, which has sold millions of copies. The scientific evidence for the merits of its rapid-fire mental challenges, such as totting up the value of coins, remains unclear but Nintendo pitches these games as fine entertainment, which is certainly true.

Less coy is Lumos Labs, which sells access to a “scientifically designed brain training programme” that consists of “engaging brain games and exercises developed by leading neuroscientists” via its website www.lumosity.com for £6.95 a month.

The company states that Lumosity users have experienced clearer and quicker thinking. Perhaps so, but in tests we found the games dull. Only one title was decent – a game called Birdwatching that improves visual attention by asking you to click on a briefly appearing bird icon and remember a specific letter.

Lumosity is not worth £6.95 a month but you can give it a whirl free for seven days.

GIVE US A JOB

Many job-hunters will have encountered those dreaded psychometric tests, much loved by big companies during recruitment. They’re designed to test cognitive abilities, such as verbal, numeric, abstract and spatial reasoning. These tests are worth practising and www.psychometric-success.com has plenty of information plus free, downloadable practice tests in PDF form.

Psychometric testing is designed to assess cognitive abilities that cannot be acquired simply with practice but it is often just unfamiliarity with such tests that holds people back from demonstrating their true ability under fire. The more practice you do, the better. The company SHL offers free timed online interactive practice tests at tinyurl.com/5olotp and it also provides personal consultation.

FORGET ME NOT

Memory is a key area where online tests are both useful and motivating. One of the best is that set up by Edinburgh University for the BBC at tinyurl.com/28mudv. A key virtue of this test (and some other online resources) is that it adapts to your ability – something traditional puzzles do not. This 20-minute test measures your ability to remember shapes, numbers, words and missing objects.

The brain best remembers things such as to-do lists by the mechanism of association. Anyone can use simple techniques, known as mnemonics, that rely on an easily remembered word, phrase or rhyme whose first letters are associated with the list items. There are several free articles that explain how they work at www.mindtools.com.

There are more free mnemonic technique guides at www.memoryschool.com, and its two-week online memory course, “Developing Your Mind”, costs £20. Alternatively, Andi Bell, the world memory champion, outlines his technique of putting objects to be remembered into familiar surroundings at www.tinyurl.com/2con7. For example, picture a lamp, or other objects, littered around your garden.

Once you have mastered the technique you can practise it at www.memorise.org/memoryGym.htm, which has various memory “gym machines” to build your numerical and visual memory. The site uses animated graphics, the speed of which can be adjusted as your skills develop.

THINK OUTSIDE THE BOX

Remembering facts is one thing but the web also has superb tools for generating new ideas. The concept of mind mapping, invented in the 1960s, is now a widely used, highly effective brainstorming technique. For example, instead of making a normal list when planning, say, an event, a mind map involves drawing a swift spider diagram of keywords connected by branches – guests, entertainment and so forth – around the central theme.

New mind-mapping software has been developed and following its recent launch in Japan it became Amazon’s No 1 selling software, knocking computer games off the top spot. The software, which will be launched in the UK this summer, costs £59 ( www.imindmap.com) but has a 30-day free trial.

Fresh ideas rarely come out of the blue, but by associations created by links from other ideas. You can rely on your subconscious to do this, or cheat and use your computer. The Mind Gym’s “random idea generator” does what it says.

Once you have inputted the topic that you need ideas on, the generator fires random words or pictures at you at a speed of your choosing in the hope that one of these will spark a fresh idea by association. If you buy Mind Gym’s excellent book, Wake Your Mind Up, for £13, you get access to the website (www.themindgym.com).

Another good brainstorming tool is the “outrageous opposites generator”. This asks you questions on your chosen theme then helps you find the polar opposite, which can create workable ideas. It sounds daft but the concept led to the invention of stuffed-crust pizza.

Learning to think laterally is paramount to creative idea generation and finding unusual solutions to problems. The forum at www.lateralpuzzles.com has a huge supply of vexing lateral thinking problems set by the forum’s users themselves. These are essentially riddles that often involve solving bizarre murders or, say, how to cross a rickety bridge while carrying heavy objects.

You can follow the discussion threads to pick up clues and see which way other users have been thinking. When you think you’ve cracked a problem – or need the answer out of sheer exasperation – type “spoiler” into the search box to get the solution.

THAT’S LOGICAL

The next step is to make sure your logic is solid. A good place to begin improving your technique is www.think-logically.co.uk/lt.htm. It has a 15-question test on deductive reasoning. Once you complete each section, the theory behind it is explained.

Then move on to the excellent resource for bite-size logic and reasoning lessons at tinyurl.com/55kklp. Here, 16 separate aspects of logic and reasoning are explained, each with an interactive test and quizzes so that you can see how well you’ve grasped each principle.

Probably the best way to beef up your strategy and logic skills is with the noble game of chess; you can do so for free online at www.chesscube.com.

DO THE MATHS

Numeracy skills are easy to improve with practice and sudoku will train you in the kind of logic and problem-solving that are useful in many maths problems. At www.sudokukingdom.com you can play online free with four levels of difficulty.

Another enjoyable way to brush up on your maths is at www.counton.org/games/mathonaire. It follows the Who Wants To Be a Millionaire? gameshow format, complete with “ask the audience” and “phone a friend” equivalents.