Final week, I posed this challenge: You and 9 of your coworkers are sitting in a convention room when anyone wonders aloud concerning the group’s common wage. Everyone seems to be curious, however no one feels snug sharing their very own pay with the group. How are you going to all study your common wage with out anyone studying any extra details about one other individual’s wage (apart from what could be deduced from the group common)? You all have pen and paper and might conceal what you write from others, however you don’t have any different instruments at your disposal. You might assume that everyone cooperates with the chosen technique.
Resolution to Puzzle #23: Cash Secrets and techniques
Quantity the ten folks from 1 to 10. Particular person one thinks of a random quantity. It may be optimistic or detrimental, however ought to be massive in magnitude. Name the random quantity r, and the salaries s1, s2, …, s10. Particular person one provides their private wage to their chosen quantity (r + s1), writes down the outcome, and slides it the wrong 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 detrimental 37-digit quantity, how may they deduce what a part of it’s r and what half is s1?
Particular person two then provides their wage to the quantity they acquired from individual one (yielding r + s1 + s2), writes down the outcome, and slides it face all the way down to individual three. Once more, individual three learns nothing concerning the earlier salaries. They didn’t see r + s1, they solely see r + s1 + s2, which appears 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.
Particular person one then subtracts r from the whole, yielding simply the sum of all people’s salaries. They divide this by ten and report the common to the group.
Random numbers play an important position in digital safety and privateness in a lot the identical manner that they do on this puzzle. Randomly generated numbers can obscure delicate data in refined methods and permit researchers to scrupulously show properties of their data-protection programs.
I loved studying your inventive options to this puzzle. There have been a number of variations that I hadn’t thought of earlier than. In the event you’re serious about different strategies, I encourage you to learn final week’s comments!
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