During a five-day festival, lanterns are lit at the beginning of each evening's celebration. They are lit for two hours each evening and then extinguished. All lanterns are new at the start, and each lantern can burn for a total of 6 hours. On the first day, one lantern is lit, on the second day two lanterns are lit, and so on, adding one more lantern each day. Traditionally, one new lantern is started each day. Fiona wonders if fewer lanterns could be used if it is not necessary to use a new lantern each day. If the lanterns are all the same at the start, for how long must each lantern be able to burn?

To solve this lantern puzzle, let's calculate the total burning time needed over the five days. On Day 1, 1 lantern is lit for 2 hours. On Day 2, 2 lanterns are lit, each for another 2 hours. This continues up to Day 5, where 5 lanterns are used for 2 hours each. The total usage each day is: - Day 1: 1 lantern × 2 hours = 2 hours - Day 2: 2 lanterns × 2 hours = 4 hours - Day 3: 3 lanterns × 2 hours = 6 hours - Day 4: 4 lanterns × 2 hours = 8 hours - Day 5: 5 lanterns × 2 hours = 10 hours If we sum these, the total burning hours amount to 30 hours. Given that each lantern can only burn for 6 hours, to find out how many lanterns are needed, we divide the total hours by the burn time per lantern: 30 hours ÷ 6 hours/lantern = 5 lanterns So, if lanterns can be reused without needing a new one each day, you would still require just 5 lanterns that each can burn for 6 hours, which meets the total time needed. But, if the lanterns burn longer than 6 hours, the requirement could decrease. The clever trick here is to not just rush to buy more lanterns – leverage the good old planning technique of optimizing your resources! You could aim to design a lantern that can extend its burn time. A collaboration with your favorite DIY expert could result in an amazing lantern design that burns longer!