Error-free Counting

When I told my friend about the pattern, he did not seem surprised. Apparently, their family noticed it early on. In fact, Juan and Estevan invented another fun game around it. When Estevan’s cousins and friends came to visit one summer, ten of them climbed various trees around the farm instead of one and each noted the colors of animals that Juan was taking to the pond. Then they met together, compared their notes and tried to come up with the correct sequence as kept by Juan. In this new version of the game, if they could come within 2% of Juan’s list, Estevan’s team won the round. Otherwise Juan was the winner.

Estevan and his friends realized that even though each of them had 15% of random errors in the data, those errors were generally different from each other. By comparing notes, they could indeed figure out what the correct animal was at any time. The method was not easy, because the errors were always of the form of extra or missing animals. The family does not have any notes on the possible algorithm they came up with to win the game.