Can't Find a Coin?

'Can't Find a Coin?' printed from https://nrich.maths.org/

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Nabeelah from Langley Grammar School commented that:

Your teacher won't know whether you have cheated or not because they can't know what happend because the result can be anything.

Of course this is right but your results could be suspicious if they are very unlikely to occur.

Some people suggested ways in which to get results that appeared likely.

Eloi fromSt. Patrick's Catholic Primary School went about it like this:

We used a coin for the first twenty then we did something similar to it to get our solution.

Phil used this strategy that managed to fool the computer:

I started by making them all heads. I then flipped every second coin. Then I flipped every third coin, then every 5th, 7th, 11th, 13th, 17th ... until I'd gone through all the prime numbers. The computer was sure these were random.

Thomas from High Storrs suggested this:
The best way of making the results seem random is not having equal numbers of heads and tails. If you decide to have more heads then have large groups of heads with a few tails in between in groups of three. If you alter the size of the groups of heads then the results appear random.

Philippa from Ashcroft Academy worked out that Earl had the most suspicious results:
I think Earl is the cheat because his heads and tails are pretty much equal as if he tried too hard to simulate the random pattern of a coin.

Another way of telling that Earl is the most likely cheat is to notice that he has no strings of repeated results of length of 5 or more, and when you realise that there are 95 strings of 6 consecutive results (1st, 2nd, 3rd, 4th, 5th and 6th - 2nd, 3rd, 4th, 5th, 6th and 7th - 3rd, 4th, 5th, 6th, 7th and 8th...) you may find it suspicious that long strings of repeated results do not appear at all.