Final week, I posed this challenge: You and 9 of your coworkers are sitting in a convention room when any person wonders aloud in regards to the group’s common wage. Everyone seems to be curious, however no one feels snug sharing their very own pay with the group. How will you all study your common wage with out anyone studying any extra details about one other individual’s wage (aside from what will be deduced from the group common)? You all have pen and paper and may conceal what you write from others, however you don’t have any different instruments at your disposal. You could assume that everyone cooperates with the chosen technique.
Answer to Puzzle #23: Cash Secrets and techniques
Quantity the ten individuals from 1 to 10. Individual one thinks of a random quantity. It may be constructive or destructive, however must be giant in magnitude. Name the random quantity r, and the salaries s1, s2, …, s10. Individual one provides their private wage to their chosen quantity (r + s1), writes down the consequence, and slides it the other way up to individual two.
Discover that by taking a look at the results of r + s1, individual two learns nothing about individual one’s wage. In the event that they acquired some random-looking destructive 37-digit quantity, how might they deduce what a part of it’s r and what half is s1?
Individual two then provides their wage to the quantity they acquired from individual one (yielding r + s1 + s2), writes down the consequence, and slides it face all the way down to individual three. Once more, individual three learns nothing in regards to the earlier salaries. They didn’t see r + s1, they solely see r + s1 + s2, which seems to be simply as random to them as r itself would.
This course of continues across the circle till the paper returns to individual one, now containing r + s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9 + s10.
Individual one then subtracts r from the entire, yielding simply the sum of everyone’s salaries. They divide this by ten and report the typical to the group.
Random numbers play a vital position in digital safety and privateness in a lot the identical approach that they do on this puzzle. Randomly generated numbers can obscure delicate info in refined methods and permit researchers to carefully show properties of their data-protection methods.
I loved studying your inventive options to this puzzle. There have been a number of variations that I hadn’t thought-about earlier than. When you’re fascinated with different strategies, I encourage you to learn final week’s comments!
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