Hello Everyone!
To help students understand mathematics more deeply, this puzzle could be extended by reversing the direction of the problem. Instead of having students find the weights that model the solution, they could be given a set of weights and asked to determine how many consecutive whole numbers, beginning with 1, can be measured using them. This would encourage students to identify patterns and develop a deeper understanding of why certain weights work.
This puzzle connects with number theory and bases that I am familiar with because, for the one-pan scale, each weight can either be used or not used. This is similar to the binary number system, where each digit is either 0 or 1. The weights also follow powers of 2 for the one-pan scale and bases of 3 for the two-pan scale. These bases are similar to what students know and practice in class, which forms connections between these answers and answers from previous math problems that involve the same bases.
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