Number puzzle #1

[Radio]

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 = ?

[NN5I]

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.

[Andy N1ORK]

111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 90
119 = 101
????????????
My guess, I think

[TXiceman]

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

[TimeToGetGoing]

How about...

111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 80
119 = 91

73
Bob
KV4MJ

[NN5I]

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 two-piece 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 two-digit 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?

[TXiceman]

111 = 13
112 = 24
113 = 35
114 = 46
115 = 57
116 = 68
117 = 79
118 = 810
119 = 911

Ken

[Radio]

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...

[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.

[NN5I]

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.

[wa8yxm]

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.

[NN5I]

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.