This week’s SUMS talk is being given by PhD graduand Gareth White. Abstract: A classic problem states: Given twelve coins, with 11 identical coins and one counterfeit coin with a different weight (otherwise identical), as well as a balance scale, how can you identify the counterfeit coin using only 3 weighings? I will be discussing this problem, as well as generalisations (such as determining the maximum number of coins that will allow us to identify a counterfeit coin in k weighings, etc.), and discuss how this relates to things such as Hamming Codes and Information Theory.