You want to express numbers with only one number and certain operations. As an example, let us say you have addition, multiplication, subtraction, and division (and you are allowed to use parenthesis). And you only have five numbers 2 available. You can express the numbers 1 to 10 in the following way:
Your task is to do the same, but instead of number 2, use number 5, i.e. express numbers 1 to 10 with exactly five numbers 5 and combining them with four allowed operations: addition, multiplication, subtraction, and division. You are also allowed to use parentheses.
[b]BONUS:[/b] Can you do it also for the number 23?
@sumojumo The reason I think there is some funky number theory under this is that I was able to represent 5^2 with five 23's but not 5. But then I was able to represent 5 with five 5's.
@CopperCicada yes, there might quite as well be something fishy going on. This is a hard problem where actually quite interesting combinatorial patterns occur. I was playing around a little bit and a huge conundrum is starting to happen very quickly - so extrapolating any formulas is definitely not straightforward if not impossible in certain cases
@CopperCicada Just to give you some feedback on 23 - it is actually not possible to do it with 23, no number between 5 and 10 can be done. But you can do 11,12, 20,21,..
@SW-User unfortunately just a little bit later than the winner, but thank you very much for playing, you got some number a bit different than the other solution.👍️
@Jackaloftheazuresand absolutely not too dumb, my fault for posting an ambiguous bonus question. What I mean is express 23 with five 5s. But what you started with 23s is an interresting challenge, which I am too lazy to start solving by hand, but will tell you if it is even possible tomorrow (with a little help from my friend the PC ;)).
@windinhishair congratulations for 23, and apologies if it was a bit ambiguous for some, I meant how do you express 23 with five 5s. But it would be probably a challenge also for five 23s :). I have a computer program that does that for me, so I can tell you the results tomorrow :)
@SW-User sorry, next time I will tag you immediately :)
SW-User
@sumojumo I can be kind of random about them, sometimes I'm all up for it and sometimes I'm just too mentally exhausted, but I always like to see them and people's solutions.
@SW-User oh, I am like that as well. Actually, I am more of an avid puzzle maker than I am a puzzle solver. Probably too lazy to solve, that is why I am a programmer, we like to automate things because we do not like doing them :D
@Miram My deepest apologies Miram, I did read your and wanted to give you a more thoughtful reply. I just send you a reply at the same moment you read this. BTW, to everyone else playing, Miram was the first one to answer correctly to my PM, she is just such a great sports that she said she wanted someone else to answer first. Kudos to Miram
