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dice collection updated!

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I added a problem, #57 of now 80 problems. It is the problem of creating a single die with distinct integer faces such that when we roll twice, sum and add one, we always get a prime. This is really just a simpler version of problem 56, but I thought I would add it anyway, since it's kind of fun.

https://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf

update to my dice problem collection

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Updated my dice problem collection. The new problem is problem 40: A die is rolled and summed repeatedly until the sum is 100 or more. What is the most likely last roll? What if we roll two dice at time? Three, etc.?

If one die is rolled, then 6 is the most likely last roll, while 7 is the most likely last roll when two dice are rolled. With three dice, the most likely last roll is 12, but for more dice, a very clear pattern emerges: if the number of dice rolled is odd, then the most likely last roll is the most likely roll (greater than the median), while for an even number of dice, it is one more than the most likely roll. (Here we assume a sufficiently large value for "100": for large numbers of dice, we want to extend the threshold so the analysis is smoother.)

new dice problem

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Just updated my Collection of Dice problems with a problem suggested by a reader (it's #27 of the now 78 problems).

Collection of Dice Problems

Disquiet Junto 0601

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For Disquiet Junto 601, I threw a die in my bathtub and recorded the throws with an AT822 stereo microphone (through a Zoom H5) that I bought (used) years ago but had never used (I’m not really much of a microphone person). Then, using Csound, I placed copies of each recording across about 3.5 minutes, with various densities, filtering, playback speeds and amplitudes. The rolls determined for how much of the piece each recording appears: the rolls were 3,5,6,5,6,3, so the 6 rolls appear throughout, the 5’s appear up to 5/6 of the piece and the 3’s cut off at the half-way point.

More info on Disquiet Junto 601: Disquiet Junto 0601