little math problem(s) May 2022

[pier4r]

As usual, solve it with your preferred system!

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Someone gives you a closed chain composed by 23 links. The person asks you to give a sequence of 3 whole numbers between 2 and 23 (extremes included), throgh which one can jump through all jumps of the chain, starting from 1.

Example {2,2,3} with 23 links. Following the sequence the result would be:
{1, 3 (+2), 5 (+2), 8 (+3), 10 (+2), 12 (+2), 15 (+3), 17, 19, 22, 2, 4, 7, ... }

Which sequences ensure that all links are touched at least once?

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What if for a chain of length N? Say with N from 9 to 100 ? (of course one can generalize the length of the chain and the length of the sequence of jumps)

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Then two not on this website:

https://somethingorotherwhatever.com/oeisle/

OEISLE: guess the OEIS sequence (there are some bugs at times)

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https://isthisprime.com/game2/ Prime Run. I think this is playable with a non-programmable calculator.

One starts with a random whole number, that can be factored (or it is a prime) and has to get to a target number T. The objective is to (a) get to T, (b) get to T in the smallest numbers of steps (if there are multiple ways, then are all good).

Say we start with the number N, with factors F1 to Fk . To this N we can decide to add (or subtract) a factor. Thus we get to, say, N1 = N+F1 . N1 can have factors as well that can be added or subtracted to it.

Example:
Start: 186; Target:126.
186 can be written as 31*3*2 .
Thus we could: add or remove 2, add or remove 31, add or remove 3
We remove 31 and we get to 155.
155 is 31*5
Thus again we can add or remove 31 or add and remove 5.
And so on, until we get to 126.

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Question: Do you know other "games" a la prime run that could be played on a non programmable calculator?

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This site is somewhat unknown but it has nice ideas: https://somethingorotherwhatever.com/