Guest Posted October 11, 2009 Report Share Posted October 11, 2009 You have two numbers, 9 and 20. Can you make 6? You must use each of the two numbers exactly once. You can use math operations: +, -, x, /, exponents, roots or factorials. You can combine (concatenate) original numbers: e.g. 9 & 20 make 920 or 20 & 9 make 209 You cannot combine any numbers besides the original ones, split any number into separate digits, turn numbers upside down, approximate, truncate, use summations or any math operations beyond the ones stipulated above. Have fun! Quote Link to comment Share on other sites More sharing options...
0 plainglazed Posted October 11, 2009 Report Share Posted October 11, 2009 Reveal hidden contents (9.5)! x 200 ? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 Bit confused about the must use each number exactly once because if you put them together to make 209 surely thats all you can do? Anyway heres one way of doing it using them more then once. ((9/20*20/9)+(9/20*20/9)+(9/20*20/9)+(9/20*20/9)+(9/20*20/9)+(9/20*20/9)) = 6 Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 11, 2009 Report Share Posted October 11, 2009 (edited) Reveal hidden contents (fortiethroot(920))! Edited October 11, 2009 by superprismatic Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 using 9 seven times and 20 five times... Reveal hidden contents (√9 + 9)20 / [(9 + 20/20)(20-9-9)(20-9-9)] not too fond of that use them only once rule Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 (edited) Reveal hidden contents (sqrt 9)! * 2^0 That's my answer. It's pretty close to the first submission. Edited October 11, 2009 by Mr. Wiggin Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 My intention was that you get to use only the two given numbers. Otherwise it would be trivial: I could pull a 5 (or a five) of my own out of a hat and come up with 20 - 9 - 5 = 6. So you can't use a 5 or a 0, or a 40 (even if you spell it out). Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 11, 2009 Report Share Posted October 11, 2009 Reveal hidden contents What is the smallest positive integer that (xthroot(920))! can be for positive integer x? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 On 10/11/2009 at 10:48 PM, superprismatic said: Reveal hidden contents What is the smallest positive integer that (xthroot(920))! can be for positive integer x? Reveal hidden contents Ya had to find a way to sneak in that fortieth root, didn't ya? I guess that's one solution! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 Reveal hidden contents sqrt(((sqrt(9))!)! / 20) Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 11, 2009 Report Share Posted October 11, 2009 (edited) On 10/11/2009 at 11:14 PM, psychic_mind said: Reveal hidden contents sqrt(((sqrt(9))!)! / 20) FOUL! sqrt uses 2 (much like fortieth root uses 40). Edited October 11, 2009 by superprismatic Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 Reveal hidden contents don't know how to do the symbols, but would (square root of 9)! x 20 to the zeroth power work? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 11, 2009 Report Share Posted October 11, 2009 On 10/11/2009 at 11:23 PM, Patouie said: Reveal hidden contents don't know how to do the symbols, but would (square root of 9)! x 20 to the zeroth power work? Reveal hidden contents See my second post. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 Woah, that's cool 202020 = 2*3*5*7*13*37 Reveal hidden contents Using 8 of the numbers: (20*9 - 99 - 9 - 9 -9)/9 Using 7: log(9+9+9+9) base (20 - 9 - 9) 7 again: (920 + 9*20 - 20)/9/20 7 again! (20-9-9)*(log(9*9*9) base 9) Can't get it less than 7 yet Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 On 10/11/2009 at 11:14 PM, psychic_mind said: Reveal hidden contents sqrt(((sqrt(9))!)! / 20) Reveal hidden contents You read my mind! That's the one I was thinking of too. Maybe there are others -- I don't know. . Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 Took me a while to wade through the parentheses, Psychic Mind. That's a lovely, clean solution! Kudos! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 On 10/12/2009 at 3:23 AM, xamdam said: You read my mind! That's the one I was thinking of too. Maybe there are others -- I don't know. Your intention might be to allow square-roots but you didn't mention that in the original questions. You simply said roots. And you denied some of the answers by pointing out that they used fortieths root and hence used the not-given number forty. Similarly can't I argue that you used twoth root and hence used the not-given number 2? I know you could have always escaped this problem by using the term "square-root", rather than just "root" in your OP. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 what about... Reveal hidden contents ((20-9-9)*sqrt 9 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 On 10/12/2009 at 7:45 AM, the-genius said: Your intention might be to allow square-roots but you didn't mention that in the original questions. You simply said roots. And you denied some of the answers by pointing out that they used fortieths root and hence used the not-given number forty. Similarly can't I argue that you used twoth root and hence used the not-given number 2? I know you could have always escaped this problem by using the term "square-root", rather than just "root" in your OP. I guess I've never put a 2 in the little crook of the root symbol for square root -- to me, no number there meant the default = square root. Hmmmm. I didn't actually want to restrict it to square roots. When I write the cube root of 8, I would use two numbers -- an 8 inside and a 3 in the crook. Are these not standard forms? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 12, 2009 Report Share Posted October 12, 2009 On 10/12/2009 at 2:03 PM, xamdam said: I guess I've never put a 2 in the little crook of the root symbol for square root -- to me, no number there meant the default = square root. Hmmmm. I didn't actually want to restrict it to square roots. When I write the cube root of 8, I would use two numbers -- an 8 inside and a 3 in the crook. Are these not standard forms? The only roots we can use are the 9th root of x and the 20th root of x, unless of course you make another number first (do 20-9 and now you can take the 11th root of something) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2009 Report Share Posted October 14, 2009 Reveal hidden contents ( ( (sqrt(9))! )! / ( (sqrt(9))! ) ) / 20 Or in other words, (x! / x) / 20 ; where x = 6 = (sqrt(9))! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2009 Report Share Posted October 14, 2009 Reveal hidden contents Somewhat mindless ways of getting it down to 6 numbers used: (9*20-20-20-20)/20 (9*9-9-9-9)/9 And 5 used! 920/20-20-20 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2009 Report Share Posted October 14, 2009 On 10/14/2009 at 6:21 PM, JacKH said: Reveal hidden contents ( ( (sqrt(9))! )! / ( (sqrt(9))! ) ) / 20 Or in other words, (x! / x) / 20 ; where x = 6 = (sqrt(9))! Reveal hidden contents It makes 6, but... it uses the 9 twice. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2009 Report Share Posted October 14, 2009 On 10/14/2009 at 7:51 PM, DarthNoob said: Reveal hidden contents Somewhat mindless ways of getting it down to 6 numbers used: (9*20-20-20-20)/20 (9*9-9-9-9)/9 And 5 used! 920/20-20-20 Reveal hidden contents It's getting there. Gotta get it down to only one 9 and one 20 now. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 15, 2009 Report Share Posted October 15, 2009 Oops..sorry! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 20, 2010 Report Share Posted March 20, 2010 Reveal hidden contents ((sqrt9)!)x(20^0) Quote Link to comment Share on other sites More sharing options...
Question
Guest
You have two numbers, 9 and 20. Can you make 6?
You must use each of the two numbers exactly once.
You can use math operations: +, -, x, /, exponents, roots or factorials.
You can combine (concatenate) original numbers: e.g. 9 & 20 make 920 or 20 & 9 make 209
You cannot combine any numbers besides the original ones, split any number into separate digits,
turn numbers upside down, approximate, truncate, use summations or any math operations beyond the ones stipulated above.
Have fun!
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