[Guest]

1) You have 8, 13, 15 and 20. Can you make 9?

Use each of the four numbers exactly once to make a numerical expression = 9.

You can use ( ), +, -, x, /, exponents, factorials and square roots. You are not required to use a 2 when indicating a square root.

You can combine (concatenate) original numbers: e.g. 13 & 8 to make 138.

You cannot combine any numbers besides the original ones, split any number into separate digits,

turn numbers upside down, approximate, truncate, use summations, limits or any math operations beyond the ones stipulated .

Here are a couple others:

2) You have 7, 13, 19 and 23. Can you make 26?

3) You have 6, 8, 13, and 19. Can you make 17?

Can they be done?

#1 and #2 each have at least two unique solutions.

I'm not sure about #3 -- I couldn't figure it out.

(In the case that nobody gets #3, I'll leave it to DeeGee to prove no solution exists.)

[plainglazed]

13-sqrt(8)^(20/15)

[Guest]

13-sqrt(8)^(20/15)

Now I know of three ways to get #1

[plainglazed]

(7!/sqrt(13+23)!) + 19 = 26

[Guest]

that was my first way, also, for #2

By the way, most of my relatives are from NC. My grandpa used to tell me about hiking in the Smoky Mountains.

Edited November 24, 2009 by xamdam

[Guest]

9 = 15 - (13-8)! / 20

[Guest]

9 = 15 - (13-8)! / 20

that was my second way to get #1

[Guest]

for 3, i don't know if this is allowed, but...

concatenate 13 and 6

136/8=17

then multiply by sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(...sqrt(19))))...))

17*1=17

[Guest]

for 3, i don't know if this is allowed, but...

concatenate 13 and 6

136/8=17

then multiply by sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(...sqrt(19))))...))

17*1=17

Clever. I guess you could make a one out of any positive integer with that trick. I suppose some might argue that you're bending the "limit" constraint in the O.P.

[Guest]

Your other puzzle got me thinking...

(8!! - 6!! - 13) / 19

Edited February 18, 2010 by ljb

[Guest]

Your other puzzle got me thinking...

(8!! - 6!! - 13) / 19

So 8!! is a way of representing 8*6*4*2 then.

It seems like I get a lot of my ideas for new codes on my failed attempts to solve yours.

Good job factorial!

[Guest]

So 8!! is a way of representing 8*6*4*2 then.

*shrug* To be honest I didn't know about double factorials until today. However, Wolfram Alpha recognizes the string, so I will consider it valid.