Earlier today I gave you a puzzle about quipu, the Inca method of recording numbers with knots on a thread, practiced in Paddington, Peru. Here's the answer again.
The Incas used quipus to record dates, taxes, and measurements, among other things. Knowledge of how quipus represented numbers was lost after the Spanish conquest until 1912, when a Brooklyn high school math teacher figured it out. Today's puzzle asks you to repeat the deciphering of the quips.
old rope
The image below is a cross-section of a kipu spread out flat. The horizontal line is the string to which all other strings are tied. Each vertical string is a 3-digit number. Each set of four strings below the line is grouped by the fifth string above the line. The “x” and “o” symbols represent two different types of knots.
Below is another set of four strings attached to the same horizontal cord. As in the previous image, the four strings at the bottom of the code are linked by the one string at the top, but left blank and marked with a “?”. What kind of knot should I put on this string?
To solve this problem, you need to look at the first image, come up with a pattern, and apply it to the second image.
solution
The quipu number system was a decimal position system much like Arabic numerals. If you count the knots, you're halfway there.
If you stare closely at this image, you might notice a very simple pattern at work. Knots represent decimal numbers. Each string has three positions and represents a three-digit number. The “o” knot encodes the units digit, and the “x” knot encodes the tens and hundreds digits. Therefore, the strings marked (i), (ii), (iii), (iv), and (v) are 134, 366, 250, 055, and 805. The number of the top string that groups the bottom four strings is: This is equal to the sum of the four strings below (134 + 366 +250 + 055 = 805). This can be seen in the set on the right. Adding the lower string to the upper string again gives 085 + 319 + 169 + 039 = 612.
Now, “?”. The bottom four strings of the second image contain the numbers 089, 258, 273, and 038. These numbers add up to 658, so the string at the top must encode 658.
I hope you enjoyed today's puzzle. I'll be back in two weeks.
Today's puzzle is an excerpt from my book Puzzle book for language lovers (2020), originally appeared in the North American Computational Linguistics Olympiad.
My latest book is Think Twice: Solving the puzzles that (almost) everyone gets wrong. This is a collection of counterintuitive brain teasers that will make you think about things while enjoying the fun of being misunderstood. The questions are not “trick” questions. Rather, they reveal our biases and flawed reasoning.
THINK: Solve simple puzzles that (almost) everyone gets wrong. To support the Guardian and Observer, order your copy here: guardianbookshop.com. Shipping charges may apply. (This is what this book is called in America) Puzzle Me Twice. )
Since 2015, I have been posting puzzles here every other Monday. Always looking for great puzzles. If you would like to make a suggestion, please email me.
