Category Archives: problems and puzzles

What’s so special about {0,2,3,4,7,11,12,14}?

Three postings here (1, 2, 3) have discussed what happens when you form all pairwise sums and differences from a finite set of integers. The number of differences almost always exceeds the number of sums—a fact that lends special interest … Continue reading

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Sums, differences, and surprises

I’ve received the following note from Barry Cipra, bit-player’s Bureau Chief in Northfield, Minnesota, (where all hail broke loose yesterday): Your latest postings [here and here] have motivated me to idle away some time with a variant of the problem(s) … Continue reading

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More on sums and differences

Kevin O’Bryant, whose work on sets that have more sums than differences was mentioned in this recent post, writes as follows: Here’s a related problem that Mel Nathanson and myself (with Ruzsa and a few students) have also been thinking … Continue reading

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Counting sums and differences

Take a set of integers, say {0, 2, 5, 8, 11}, and write down all the numbers that can be represented as sums of two elements drawn from this set. For our example the answer is {0, 2, 4, 5, … Continue reading

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The oddest numbers

At the library the other day I was perusing the Collected Rantings and Ravings of Edsger W. Dijkstra [Note 1]. While leafing through the pages in search of something else [Note 2], I stumbled across “An Exercise for Dr. R. … Continue reading

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