
05292013, 12:56 PM

#1

Administrator
Join Date: Nov 2007
Location: Fayetteville, GA, USA
Posts: 3,017

Number puzzle #1
This was going around in the email at work. 24 hour rule.
And I got it wrong.
If you are not good at thinking or math this might be a bit difficult. If your calculations are wrong in the beginning it will compound the effects in the end.
111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = ?
117 = ?
118 = ?
119 = ?



05292013, 11:48 PM

#2

Carl, nn5i
Join Date: Sep 2011
Location: Tallahassee, FL
Posts: 1,441

There is more than one solution, depending upon what algorithm you select. At least two different algorithms, probably more, will yield the given results for the first five rows, and identical results for the sixth and seventh rows, but yield different results for the last two (eighth and ninth) rows.
__________________
 Carl



05302013, 04:28 AM

#3

Senior Member
Join Date: Jan 2008
Location: Manchester, CT
Posts: 1,034

111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 90
119 = 101
????????????
My guess, I think
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Hello anyone out there?
Is this thing on?
SkyWarn, CERT, EmComm



05302013, 07:45 AM

#4

Senior Member
Join Date: Nov 2007
Location: Near Houston, TX
Posts: 553

My brain over heated and all of the smoke was let out. But my wife says I was full of something other than smoke.
Ken
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KE5DFR
2013 HitchHiker Champagne 38RLRSB, 2012 F350 Dually crew cab, 6.7L,
Mobile Yaesu FT857D w/ Lil' Tarheel II antenna and Larsen dual bander, Turbo Tuner.
Base unit...Kenwood TS480HX, LDG AT200 Pro tuner, Eagle One Vertical and Windom 80 meter dipole.
Standard Schnauzer..her call is K9WOOF



05302013, 08:44 AM

#5

Junior Member
Join Date: Mar 2013
Location: Montclair, VA
Posts: 22

How about...
111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 80
119 = 91
73
Bob
KV4MJ



05302013, 01:13 PM

#6

Carl, nn5i
Join Date: Sep 2011
Location: Tallahassee, FL
Posts: 1,441

OK, KV4MJ came up with another algorithm, so now there are at least three. Let's call the original number (such as 111) to be a set of three individual digits abc, where a is the hundreds digit, b is the tens digit, and c is the ones digit.
FIRST ALGORITHM
result = 10c + (a+b+c)
This gives:
111 > 13
112 > 24
113 > 35
114 > 46
115 > 57
116 > 68
117 > 79
118 > 90
119 > 101
SECOND ALGORITHM
Result = a twopiece string. The first piece is always one digit, and is the third digit (c) of the input. The second piece is one or two digits, equal to the sum of the three input digits (a+b+c).
This gives:
111 > 13
112 > 24
113 > 35
114 > 46
115 > 57
116 > 68
117 > 79
118 > 810
119 > 911
THIRD ALGORITHM (KV4MJ's algorithm as I see it)
Result = a twodigit number. The first digit is just the ones digit (c) of the input. The second digit is the ones digit of the sum of the three input digits (a+b+c).
This gives:
111 > 13
112 > 24
113 > 35
114 > 46
115 > 57
116 > 68
117 > 79
118 > 80
119 > 91
Any of these, and probably many more, will meet the requirements stated in the problem. What algorithm did you have in mind, Wade?
__________________
 Carl



05302013, 02:42 PM

#7

Senior Member
Join Date: Nov 2007
Location: Near Houston, TX
Posts: 553

111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 810
119 = 911
Ken
__________________
KE5DFR
2013 HitchHiker Champagne 38RLRSB, 2012 F350 Dually crew cab, 6.7L,
Mobile Yaesu FT857D w/ Lil' Tarheel II antenna and Larsen dual bander, Turbo Tuner.
Base unit...Kenwood TS480HX, LDG AT200 Pro tuner, Eagle One Vertical and Windom 80 meter dipole.
Standard Schnauzer..her call is K9WOOF



05302013, 09:25 PM

#8

Administrator
Join Date: Nov 2007
Location: Fayetteville, GA, USA
Posts: 3,017

Quote:
Originally Posted by NN5I
Any of these, and probably many more, will meet the requirements stated in the problem. What algorithm did you have in mind, Wade?

I used the same algorithm Ken did. And I was deemed wrong.
This is so much fun! I'll let you guys work in it another day...



05312013, 04:35 PM

#9

Administrator
Join Date: Nov 2007
Location: Fayetteville, GA, USA
Posts: 3,017

I was informed the correct formula to solve the puzzle is as follows.
11a = (11 x a) + 2 = n, such that...
111 = (11 x 1) + 2 = 13
112 = (11 x 2) + 2 = 24
and so on until
118 = (11 x 8) + 2 = 90
119 = (11 x 9) + 2 = 101
And as I said I got it wrong. I used Carl's second algorithm, where 11 is multiplied by the given variable and then you add the sum of the digits.
"Carl's Second Algorithm" does sound like something from a dusty old physics book, doesn't it? Right up there with Newton's Second law of Thermodynamics.



05312013, 06:01 PM

#10

Carl, nn5i
Join Date: Sep 2011
Location: Tallahassee, FL
Posts: 1,441

Quote:
Originally Posted by Radio
I was informed the correct formula to solve the puzzle is as follows.
11a = (11 x a) + 2 = n, such that...
111 = (11 x 1) + 2 = 13
112 = (11 x 2) + 2 = 24
and so on until
118 = (11 x 8) + 2 = 90
119 = (11 x 9) + 2 = 101
And as I said I got it wrong. I used Carl's second algorithm, where 11 is multiplied by the given variable and then you add the sum of the digits.
"Carl's Second Algorithm" does sound like something from a dusty old physics book, doesn't it? Right up there with Newton's Second law of Thermodynamics.

(1) Your answer was just as right as any other that gives the correct results for the first five lines. It wasn't wrong in any sense of the word.
(2) Forgive me; there is a Second Law of Thermodynamics, but it has nothing whatever to do with Newton's Second Law.
Second Law of Thermodynamics: the entropy of an isolated system never decreases. It may increase, and almost always does; but if it remains constant, every process going on in the isolated system is thermodynamically reversible. In nature, reversible processes are rare.
Newton's Second Law (of motion): f=ma, force = mass times acceleration.
F, m, and a are all vector quantities.
__________________
 Carl



06012013, 09:50 AM

#11

Senior Member
Join Date: Nov 2007
Location: Mobile, on the road
Posts: 1,139

If there is more than one solution to the problem, then the problem is that the problem is not precise enough and the correct answer is "Not enough information to solve"
Math should have just one or two answers,,, The two are Plus or Minus
Example. The square root of FOUR is Plus, or Minus TWO.



06012013, 06:35 PM

#12

Carl, nn5i
Join Date: Sep 2011
Location: Tallahassee, FL
Posts: 1,441

And four, like everything else, has three cube roots and four fourth roots, etc. So it ain't so that everything must have one or two solutions.
__________________
 Carl




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