mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2007-09-21, 22:43   #1
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

23·1,117 Posts
Default Four 1's puzzle

Figured I would start this one.

Like the 4 4's.

Using four 1's and standard mathematical operations formulate equations with the answer being each of the numbers from 0 to 100 and on.

Every calculation MUST use exactly all four 1's and no other digits.

The allowable operations are:

Class 1
  • Addition: 1 + 1 = 2
  • Subtraction: 1 – 1 = 0
  • Multiplication: 1 * 1 = 1
  • Division: 1 / 1 = 1
  • Parenthesis: (1 + 1) / 1 = 2
  • Concatenation: 111
  • Decimal Point: .1

Class 2
  • Factorial: 11! = 39916800
  • Exponential: 11^11 = 285311670611
  • Square-root: √11 = 3.3166247903553998491149327366707

Class 3
  • Absolute value: |-1| = 1
  • gamma: ?

Solution scoring:
100 points per class 3 operator
10 points per class 2 operator
1 point per class 1 operator (parenthesis per pair), except the following:
1/2 point per decimal
0 points for concatenation

The goal is to get as low as score solution as possible.


First 3 to start:

0 = 11 - 11
1 = 11 / 11
2 = 1/1 + 1/1

Last fiddled with by Uncwilly on 2007-09-21 at 22:47
Uncwilly is online now   Reply With Quote
Old 2007-09-21, 23:35   #2
Mini-Geek
Account Deleted
 
Mini-Geek's Avatar
 
"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts
Default

I'm putting the score for it next to the number.

A few in order:
3, 3 = 1 * 1 + 1 + 1
3, 4 = 1 + 1 + 1 + 1

And some easy ones out of order:
2, 9 = 11 - 1 - 1
3, 10 = 11 - (1 * 1)
2, 11 = 11 * 1 * 1
3, 12 = 11 + (1 * 1)
2, 13 = 11 + 1 + 1
1, 22 = 11 + 11
1, 110 = 111 - 1
1, 111 = 111 * 1
1, 112 = 111 + 1
1, 121 = 11 * 11
0, 1111 = 1111
10, 285311670611 = 11 ^ 11

I'm not so sure that very many numbers can be made with four 1's, just because of how it's so low and many operations don't, or barely, change the number you start with.
Mini-Geek is offline   Reply With Quote
Old 2007-09-22, 01:40   #3
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

5×11×107 Posts
Default

10 = 11 - 1 / 1 (2 points)
12 = 11 + 1 / 1 (2 points)
100 = 11 / .11 (1.5 points)
retina is offline   Reply With Quote
Old 2007-09-22, 03:27   #4
Kevin
 
Kevin's Avatar
 
Aug 2002
Ann Arbor, MI

433 Posts
Default

I agree that we need to add at least one degree of fudging to get everything as as combination of some fixed amount of 1's. I was thinking different number bases, but sadly b=11_b-(1_b*1_b) for all b>1.
Kevin is offline   Reply With Quote
Old 2007-09-22, 04:12   #5
Mr. P-1
 
Mr. P-1's Avatar
 
Jun 2003

7×167 Posts
Default

5 = (1 + 1 * 1)/.1 (4.5 points)
6 = (1 + 1 + 1 * 1)! (14 points)
7 = (1 + 1 + 1)! + 1 (14 points)
8 = 1/.1 - 1 - 1 (3.5 points)
Mr. P-1 is offline   Reply With Quote
Old 2007-09-22, 05:23   #6
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

5×11×107 Posts
Question

Quote:
Originally Posted by Mr. P-1 View Post
5 = (1 + 1 * 1)/.1 (4.5 points)
Really? I get 20 for that sum. What did I do wrong?
retina is offline   Reply With Quote
Old 2007-09-22, 05:26   #7
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

5·11·107 Posts
Default

5 = 1*1/(.1+.1) (5 points)
10 = 11/1.1 (1.5 points)
20 = 1/.1+1/.1 (4 points)
24 = (1+1+1+1)! (14 points)
30 = (1+1+1)/.1 (4.5 points)
55 = 11/(.1+.1) (4 points)
60 = (1+1+1)!/.1 (14.5 points)
109 = 11/.1-1 (2.5 points)
1110 = 111/.1 (1.5 points)
\infty = 11/(1-1) (3 points)

Last fiddled with by retina on 2007-09-22 at 06:13
retina is offline   Reply With Quote
Old 2007-09-23, 04:55   #8
Mr. P-1
 
Mr. P-1's Avatar
 
Jun 2003

7·167 Posts
Default

Quote:
Originally Posted by retina View Post
Really? I get 20 for that sum. What did I do wrong?
You didn't. I did. (Sigh)

I also had (1 + 1 + 1)! -1 for five, but your solution is even better.

Has anyone been able to get 14?
Mr. P-1 is offline   Reply With Quote
Old 2007-09-23, 06:10   #9
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

16FD16 Posts
Default

-1 = 1/.1 - 11 (2.5 points)
21 = 1/.1 + 11 (2.5 points)

Uncwilly, this puzzle is really hard. I hope you plan on eventually posting the solutions, because I think everyone is stuck. There must be something fundamental that we all seem to have missed so far. So many gaps in the range 0-100. Perhaps a small hint is in order.
retina is offline   Reply With Quote
Old 2007-09-24, 04:02   #10
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

588510 Posts
Default

99 = 1/.1/.1-1 (4 points)
101 = 1/.1/.1+1 (4 points)
200 = (1+1)/.1/.1 (5 points)
719 = (1+1+1)!!-1 (24 points)
720 = (1+1+1)!!*1 (24 points)
721 = (1+1+1)!!+1 (24 points)
1000 = 1/.1/.1/.1 (4.5 points)
1100 = 11/.1/.1 (3 points)

I can't see how √, || or gamma can be useful. Is that a clue as to how to generate the missing values in the 0-100 range?
retina is offline   Reply With Quote
Old 2007-09-24, 06:00   #11
Kevin
 
Kevin's Avatar
 
Aug 2002
Ann Arbor, MI

433 Posts
Default

Quote:
Originally Posted by retina View Post
99 = 1/.1/.1-1 (4 points)
101 = 1/.1/.1+1 (4 points)
200 = (1+1)/.1/.1 (5 points)
719 = (1+1+1)!!-1 (24 points)
720 = (1+1+1)!!*1 (24 points)
721 = (1+1+1)!!+1 (24 points)
1000 = 1/.1/.1/.1 (4.5 points)
1100 = 11/.1/.1 (3 points)
Just as a minor point, you probably want to write it at ((1+1+1)!)!. Usually !! is taken to mean n(n-2)(n-4)... (http://mathworld.wolfram.com/DoubleFactorial.html).

Also, gamma can be useful if you wanted to get (n-1)! instead of n! without wasting a 1.

Last fiddled with by Kevin on 2007-09-24 at 06:12
Kevin is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Some puzzle Harrywill Puzzles 4 2017-05-03 05:10
a puzzle bcp19 Puzzles 18 2012-03-02 04:11
4 4s puzzle henryzz Puzzles 4 2007-09-23 07:31
Dot puzzle nibble4bits Puzzles 37 2006-02-27 09:35
now HERE'S a puzzle. Orgasmic Troll Puzzles 6 2005-12-08 07:19

All times are UTC. The time now is 01:44.

Thu Dec 3 01:44:40 UTC 2020 up 83 days, 22:55, 1 user, load averages: 2.46, 2.12, 1.89

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.