Earlier today I set you a puzzle about a ‘khipu’, the Incan method of recording numbers with knots on string that features in Paddington in Peru. Here it is again with the answer.
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 asked you you to repeat his decipherment.
Old rope
The image below is a section of a khipu laid out flat. The horizontal line is the 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?
To solve this problem, you need to look at the first image, work out the pattern, and then apply it to the second image.
Solution
The khipu number system was a base ten, positional system much like Arabic numerals. If you count the knots you are half way there.
After some staring at this image, you might notice the very simple pattern at work. Knots represent decimal digits. Each string has three positions, and represents a three-digit number. The ‘o’-knots encode the units digits, and the ‘x’-knots encode the tens and the hundreds digits. So the strings marked (i), (ii), (iii), (iv) and (v) are 134, 366, 250, 055 and 805. The number on the top string, which groups the four bottom strings together, is equal to the sum of the four bottom strings (134 + 366 +250 + 055 = 805.) We can confirm this with the set on the right. The bottom strings again add up to the top one: 085 + 319 + 169 + 039 = 612.
Now to the ‘?’. The four bottom strings on the second image contain the numbers 089, 258, 273 and 038. These numbers add up to 658, so the top string must encode 658.
I hope you enjoyed today’s puzzle. I’ll be back in two weeks.
Today’s puzzle is extracted from my book The Language Lover’s Puzzle Book (2020), and originally appeared in the North American Computational Linguistics Olympiad.
My latest book is Think Twice: Solve the Puzzles That (Almost) Everyone Gets Wrong, a collection of counter-intuitive conundrums that make you think about thinking – while enjoying the pleasure of being misled. The questions are not ‘trick’ questions; instead, they reveal our biases and flawed reasoning.
Think Twice: Solve the Simple Puzzles (Almost) Everyone Gets Wrong. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply. (In the US, the book is called Puzzle Me Twice.)
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
