Friday puzzle: McNuggets

Last week’s puzzle was to calculate the resistance between opposite corners of a cube of identical resistors. Let’s assume they are all 1Ω since it doesn’t really matter. The key insight with this and many such problems is to find points that you know must have the same voltage (by symmetry) but which aren’t joined. You can add extra wires to join them without changing the value of the overall resistance since no current will flow in the extra wires, but they may make the calculation easier. The three corners near one terminal corner are all the same voltage, by symmetry, so consider them joined. Similarly for the three corners near the other terminal corner. This reduces the circuit to the considerably simpler one with 3 1Ω resistors in parallel, followed by 6 1Ω resistors in parallel, followed by another 3 1Ω resistors in parallel. Calculate that out and you get ⁵/₆ Ω.

McDonald’s sells chicken McNuggets in boxes of 6, 9 and 20. So you can buy 15 McNuggets by buying a box of 6 and a box of 9. But if you try you’ll find that there’s no way to buy 16. What’s the largest number of McNuggets that you can’t buy?

Answer next Friday.