The campaign, created by BD-NTWK, aims to get families to compete against each other for a chance to take a place in the national final, hosted by GMTV's Lorraine Kelly, where they will be able to win their child's university tuition fees. Footage of the final may be used in a future ad campaign.
In addition to the fees, worth the equivalent of £40,000, BD-NTWK has also secured partnerships to give competing families the chance of winning a Chrysler Grand Voyager XS or 10 Thomas Cook holidays.
The campaign will be supported by a where families can register their interest in competing.
Allan McLaughlin, associate director at BD-NTWK, said: "Through the Britain's brainiest family activity we hope to engage consumers with the product, drive awareness and encourage trial. We've designed the campaign with Nintendo, so that consumers of all ages are compelled to give it a go."
Ben Taylor, trade and promotions marketing manager at Nintendo, said: "Big Brain Academy aims to train players' brains and determine their 'Brain Weight' through a series of mind bending activities such as think, memorise, analyse, compute and identify."