In the film Paddington in Peru, which opened this weekend, the plot revolves around a string bracelet that is said to contain mystical secrets.
The bracelet is supposed to be a ‘khipu’, which was the Incan way of recording numbers. Knots were made on string, and these pieces of string were attached together in a big bundle. The Incans used khipus to record dates, taxes and measurements, among other things.
Knowledge of how khipus represented numbers was lost after the Spanish conquest, until a high school maths teacher in Brooklyn worked it out in 1912. Today’s puzzle asks you to repeat his decipherment (using an image of the same khipu he used, which is now in New York’s American Museum of Natural History).
The image below is a section of a khipu laid out flat. The horizontal line is a cord on which all other strings are tied. Each vertical string is a three-digit number. Each set of four strings below the line is grouped together by a fifth string above the line. The ‘x’ and ‘o’ symbols represent two different types of knot.
Below is another set of four strings attached to the same horizontal cord. As in the previous diagram, the four strings under the cord are linked by a single one above, which I have left blank and marked with a ‘?’. What knots should go on this string?