# Category Archives: problems and puzzles

## Jacobsthal numbers

In an item published here last May I stumbled across the sequence 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 which I dubbed “the oddest numbers” but which … Continue reading

## 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

## 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

## 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

## 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