Puzzle: Make 1-50 using only 1,2,3,4 and basic operators

[lookagain]

Outstanding! Thanks so much for your solutions. I have [finally] updated my blog with the
solutions you have provided.

From what I can see, only 133 remains without any solution, which is an amazing result considering how far we are
beyond the original scope of the first question (solve for 1-50).

Any takers for 133?

Thanks

David

DavidLeese, Denis already posted that solution for you back in post #28 in this thread.

Please use it:

133: \(\displaystyle \ \ \)4!/.2 + 13



Please do not use his later solution for it (given after your post #32).

 

[DavidLeese]

Thanks for these very elegant solutions. I've made the update to 105 and added the solution for 133. I think that's everything covered - thanks for your answers, comments, questions and participation - it's been amazing to throw out a question and get such amazing responses!

Thanks

David

 

[lookagain]

137 = (3 / .1¯ + .4) / .2

Line on top of .1 is symbol for repeating; .111111111111111111.....

What d'you think Lookagain: acceptacle?

The repeating decimal wasn't specifically allowed, but I prefer this solution you have of


137 = (3 /.1¯ + .4)/.2


to the use of floor or ceiling functions for these puzzles if possible.

 

[lookagain]

Your opinion again:

FLOOR(412/3) = 137 \(\displaystyle \ \ \ \ \ \)I care about this one also, because it's compact.

Using modular division symbol:\(\displaystyle \ \ \ \ \ \) I'm not familiar with that modular division symbol.
412 \ 3 = 137

???

I can support DavidLeese keeping "FLOOR(412/3)" so as to not bring repeated decimals
into it, *or*

I can support your new solution with the repeating decimal so as to not bring floor/ceiling
functions into it.



Regardless, I care for/like the looks and creativity of both solutions for the number 137.

 

[Ishuda]

Thanks. Symbol \ seems to be acceptable:
http://www.wolframalpha.com/input/?i=x=412\3

The backward slash was also used in the BASIC program languages as a floor function, i.e. integer division. This was a looonnnng time ago and I don't know if it is still used. I haven't used BASIC in a long time.

 

[Ishuda]

...I swear by UBasic. Don't understand why everybody doesn't use it :shock:

As far as using as floor function, I think you're wrong.
Integer division only applicable to integers.
...

I kept BASIC around (along with the compiler) for years but the program I had quit working across one of the transitions from one OS to another so I looked around for another program after a while. Since I needed to install a Perl compiler for testing some code I was writing for someone who had to have the program in Perl I just starting using Perl.

Oh, and about the backslash for FLOOR - yes I think you're correct. What I should have said is that the integer division result was the equivalent of the FLOOR function for that particular case [neglecting argument types, etc].

 

[lookagain]

.1^(-2) - 34 = [(10)^(-1)]^(-2) - 34 = [(10)^(2)] - 34 = 100 - 34 = 66

My incorrect post was thankfully deleted.

 

[jonah2.0]

Beer soaked ramblings follow.

My incorrect post was thankfully deleted.

Must have drank too much beer; keep seeing that word "incorrect".

 

[greg1313]

To represent 166:

.2^(-3) + 41

4^2 / .1 + 3!

4!(3! + 1) - 2

I like all three expressions, but I see how the third one doesn't need any decimal
points or exponentiation symbols.

 

[Richard White]

1, 2, 3, 4 puzzle

Using factorials and decimals and recurring decimals I have found expressions for all the integers from 1 to 171. Stuck by 172 at present.

Richard

 

[lookagain]

Using factorials and decimals and recurring decimals I have found
expressions for all the integers from 1 to 171. Stuck by 172 at present.

Richard

You should start your own thread, because this one is of DavidLeese, and your rules are at least
different with the recurring (repeating) decimals.

That is, don't piggyback onto the OP's thread, please.

 

[ALeeNg]

Hello - my child was given this as homework (well, the numbers 1 to 30), and I've found this thread because I was struggling to make 29 - the instructions with the homework said you could only use the operators + - / and * - i.e. no factorials, no powers.

My child was only asked to do as many as possible, but later I tried to do it myself, as you do.

The answer linked to on page one (along the lines of 32-4+1) seems to me to be a total cheat - you have the number 3, not the digit 3 - writing it as 32 implies there is a 10 to multiply by.

Anyway, as far as I can tell you can do 1 to 28 and 30 by using just 1,2,3,4 and +,-,/ and * but not 29.

You can do 29 using powers - 3^(4-1) +2 - but you cannot do 29 using just the four basic operators and the numbers (as opposed to digits) 1 to 4. And 30 is as high as you can go with these rules. Please tell me if I'm wrong, it's been bugging me!

 

[Otis]

my child was given this as homework ...

... the instructions with the homework said you could only use the operators + - / and * - i.e. no factorials, no powers.

The answer linked to on page one (along the lines of 32-4+1) seems to me to be a total cheat - you have the number 3, not the digit 3 ...

It seems as though you did not read the entire thread. The distinction between "number" and "digit" has already been discussed.

:idea: The topic of this thread does not match your child's assignment. Rather than trying to change the topic of an existing thread, you ought to start your own thread. Please read the forum's guidelines and rules.

 

[Steven G]

Denis regularly tries to change the posted exercise.

Of course he does. Otherwise he can't solve the problem.

 

[Otis]

Is there another way

Yeah, do what Heron of Alexandria did; alter the number system.