Final week, I posed this challenge: You and 9 of your coworkers are sitting in a convention room when any individual wonders aloud in regards to the group’s common wage. Everyone seems to be curious, however no one feels comfy 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 particular person’s wage (aside 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. It’s possible you’ll 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 unfavorable, however must be giant 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 other way up to particular person two.
Discover that by taking a look at the results of r + s1, particular person two learns nothing about particular person one’s wage. In the event that they obtained some random-looking unfavorable 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 obtained from particular person one (yielding r + s1 + s2), writes down the outcome, and slides it face right down to particular person three. Once more, particular person three learns nothing in regards to the earlier salaries. They didn’t see r + s1, they solely see r + s1 + s2, which seems simply as random to them as r itself would.
This course of continues across the circle till the paper returns to particular person one, now containing r + s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9 + s10.
Particular person one then subtracts r from the full, yielding simply the sum of everyone’s salaries. They divide this by ten and report the typical to the group.
Random numbers play an important function 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 methods.
I loved studying your artistic options to this puzzle. There have been a number of variations that I hadn’t thought of earlier than. In the event you’re all for different strategies, I encourage you to learn final week’s comments!
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