Summer probabilities
The workings: As it has become a tradition, the IMUS blog is taking a summer break. Whether it is deserved or not is up to our (dear) readers to decide. And as in previous years, […]
Month: July 2020
Solution: Summer probabilities
We publish here the solution to the summer probabilities divertimento. The fun: Anna and Beatrice are playing a heads or tails coin game, tossing alternately. When Anne has tossed for the \((n+1)\)-th time, they have to […]
Gilbreath’s conjecture
We consider the sequence of primes in a row. Below we write the differences between them: $$\begin{array}{ccccc cccccccccc} 2&&3&&5&&7&&11&&13&&17&&19\\ &1&&2&&2&&4&&2&&4&&2\\&&1&&0&&2&&2&&2&&2\\&&&1&&2&&0&&0&&0\\&&&&1&&2&&0&&0\\&&&&&1&&2&&0\\&&&&&&1&&2\\&&&&&&&1\end{array}$$ We continue the process by forming a third row, but subtracting the smaller from the […]
Time of crisis
“Adversity makes us wiser; prosperity destroys our appreciation of what is fair.” – Seneca. “We are in a time of crisis”: a phrase that is repeated, perhaps by every human generation. Who are we? Who […]