Make 10

[leonid]

I'm pretty sure some of you have been curious about the list of random numbers in my signature. I'll tell you what this is about.



Before that, I need to describe the rules of a game called Make 10:

(1) Pick a number between 1000 and 9999.
(2) Use +, -, x, /, parentheses, square root, and factorial (e.g. 5! = 5x4x3x2x1 = 120) to change the number into 10.
(3) You can put multiple digits together to form a number. (e.g. 4232 -> 42-32 = 10)
(4) You cannot scramble the order of the digits. (e.g. Not allowed: 3650 -> 6350 -> 6/3x5+0=10)
(5) You cannot apply rule (3) after performing an operation. (e.g. Not allowed: 5302 -> (5-3) 0 2 -> 202 -> 20/2 = 10)



Here are some examples showing how this works:

5038: 5+0-3+8 = 10
3126: -3+1+2x6 = 10
7394: 7x3-(9+R4) = 10 (R4 stands for "square root of 4" = 2)
6666: (66-6)/6 = 10
4867: 4!-(8-6)x7 = 10 (4! stands for "4 factorial" = 24)
3300: 3x3+0!+0 = 10 (0! = 1 by definition of factorial)


Now about my signature...

The following are numbers between 1000 and 9999 with which I and some people couldn't manage to make 10 using the above rules:

1667, 1766, 1767, 2100, 2101, 6067, 6076, 6077, 6176, 6177, 6607, 6617, 6667, 6670, 6671, 6677, 6706, 6716, 6717, 6760, 6761, 6766, 6768, 6771, 6778, 6788, 6876, 7066, 7166, 7176, 7177, 7578, 7606, 7607, 7660, 7661, 7670, 7671, 7677, 7706, 7707, 7760, 7761, 7766, 7776, 7826, 7886

That's right, we managed to make 10 with ALL THE REMAINING NUMBERS.


So here I made this thread hoping that someone will be able to solve any of these numbers.

Discuss!

[Wineandbread]

Re: Make 10

shoutout to zolaric for being baller at !ten

[Reincarnate]

Re: Make 10

lol I actually wrote a solver for this a long time ago, maybe I can dig it up in my old archives

[Ziergdsx18]

Re: Make 10

shoutout to zolaric for being baller at !ten

^
|
Make 10 Ranking - 1:zolaric(Wins:4387)

LOL

[Patashu]

Re: Make 10

can 0667, 0766, 0767 be solved

also petition to add Math.pow(a,b), ln and log

[leonid]

Re: Make 10

Number range is 1000 ~ 9999.
Also, the point of this is to be able to solve as many numbers as possible using as few (reasonable) operators as possible

[jimerax]

Re: Make 10

I used to do this with the number of tickets when I'm bored long time ago.

[XCV]

Re: Make 10

I have a variant of this that I like to do that's referred to as the concept of creator numbers in the world of recreational math.

Pick a number and then create it using only 1s and 2s. Factorials, parentheses, exponentiation and the four basic operations are allowed (square roots are pretty unnecessary). Example:

81 is (2 + 1)^(2 + 2), which uses four digits. I haven't been able to get any lower. Thus, 81's creator number is (for the moment, at least) 4.

Some kid has my notebook with like everything under 1000, so I can't post some of the outliers kinda like leonid's done in this thread.

[Izzy]

Re: Make 10

lol I actually wrote a solver for this a long time ago, maybe I can dig it up in my old archives

Is it just an exhaustive tester? That might be fun to code.

Let me give this a shot..

3456

3 - 4 + 5 + 6 = 10

Edit: kind of disappointed at how easy that one was.

[Reincarnate]

Re: Make 10

So I found my solver and tweaked it a bit to fit this particular problem. Do you, uh, want the full output? XD XD XD XD XD XD XD

[Izzy]

Re: Make 10

Meh, I was halfway done writing it and got bored. Doubt ill finish it later.

[Reincarnate]

Re: Make 10

For the record (just looking at the ones you have yet to solve), my solver found nothing for any of those.

[Reincarnate]

Re: Make 10

Actually there are a few here my solver didn't catch that you supposedly have solved already.

How would you do something like 1068 (something my solver missed -- and something I can't figure out manually O.o)? Not sure how to make ten from 1068. Either my program is bugged somewhere (it has a vast majority of the 1000-9999 list solved, excluding all the ones you've listed above plus a couple others) or I'm misinterpreting a rule somewhere.

[One Winged Angel]

Re: Make 10

R((-1)-0!+6)+8 works unless I broke some rule

had an 8 hour shift today and was dicking around with all the numbers in your sig in my head, leo...came up with nothing though, quite obviously

[Reincarnate]

Re: Make 10

My solver doesn't assume you can use root like that (right now it assumes that you can only apply certain items to individual numbers (N, N!, N^.5, and -N) where parentheses are used for the sake of ordering only.

So I could have A!*B! but not, say, (A+B)! but if this is legal I can easily change it. It'd imply that I could theoretically do stuff like -((A+B)!)^.5 or something, which could get annoying. The current approach is a bit more cleaner and less ambiguous but I am still curious to see the rule clarifications/approaches.

I guess we'll have to wait to see how leonid did it in order to verify the rules a bit more XD Then I can update my solver and have at it again.