The article explores two puzzles involving prime numbers, specifically concerning the calculations of powers and prices. In the first puzzle, the last digit of 3 raised to a million is determined, revealing a cycle of digits that leads to the final result of 1. The second puzzle involves a shopper buying four items for a total of 7.11, with the twist that their prices also multiply to the same total. The solutions illustrate the underlying mathematical principles and the fun nature of problem-solving with prime numbers in everyday scenarios.
When you multiply 3 by itself, the final digit of the answer cycles through the digits 3, 9, 7 and 1. Since a million is divisible by four, the final digit of 3 to the million is 1.
Let the prices be a, b, c and d. Then we know a + b + c + d = 7.11 and a x b x c x d = abcd = 7.11. We can assume that the prices in the shop are in pounds and pence, so lets multiply each of them by 100 to get rid of the decimal point.
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