Calculating Lego Combinations

By Anupum Pant

When Godtfred Kirk Christiansen was the third son of Ole Kirk Christiansen, the founder of LEGO went to the patent office to get a patent for lego blocks, he was asked a question by the patent officer to which he had no good answer. He only had an estimate. The question was – “How many combinations can 6 of the lego blocks be used to make different compound objects.”

He said he had calculated a number which was close to 102,981,000 combinations. He wasn’t quite right.
The question was so hard, that it took years to get to the exact answer. Soren Eilers, a professor of Mathematics at the University of Copenhagen put his mind to work and figured out the answer. In fact, his mind did not do him much service here. It was a computer which spit out the answer to him after a week long calculation.
He found that the actual answer to this mathematical conundrum is – 915,103,765

His computer can now calculate this number in a matter of minutes. But as you increase the number of blocks, the time needed to arrive at the answer increases hundred folds. So, the number of combinations from 7 blocks takes 2 hours. 8 blocks – around 20 days. But calculating the same for 9 blocks might take hundreds of years.

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