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/

[ijabbott]

I assume that '43' should have been a '23'?

(The answer to the puzzle seems obvious unless I'm missing something.)

[pier4r]

yes, I wanted to make an example with 43 and then I lowered it to a smaller one.

[ijabbott]

(05-29-2022 07:36 PM)ijabbott Wrote:  (The answer to the puzzle seems obvious unless I'm missing something.)

I think I was missing that there is an obvious class of solutions for the general case, but there may be other solutions that are not in the obvious class. (That does not apply when the chain length is 23 though.)