[Guest]

Sometime in the near future, we have a farmer and out of the blue a flaming object falls out of the sky into his field. A creature comes out that has a translation machine that allows him to speak English. They begin conversing until they reach a point where they ask each other their age. The farmer says he is 57 years old. The alien gives him a puzzled look and says that he himself is 212 years old, yet they appear to be about the same age. If the farmer and alien have the same amount of years and their years are equivilant, explain why they give each other two different numbers.

[Guest]

alien uses base 5

[k-man]

The alien used the numerical system with the base 5. 57 in base 5 is 212.

[Guest]

The alien used the numerical system with the base 5. 57 in base 5 is 212.

A year is determined by how many times a planet orbits a star. The farmer and the alien are from different planets

[Guest]

I was too late and everybody just beat me to answer.

Well, but can anyone tell me how did you get the answer??

I plugged in a computer... you??

[Guest]

Base 5

To arrive here, simply set-up the following chart

5^3 5^2 5^1 5^0

0 2 1 2

he is not over 125, so the next number is 25 which he has two of, followed by 5 which he has one of, and 1 which he has 2 of. 50+5+2=57

Edited June 7, 2011 by harpuzzler

[Guest]

Its 212 base 5. When converted to decimal would give 57.

[Guest]

Oh!!! Its already anwered!!! I was late ... Damn!!!!!!!!

[Guest]

A year is determined by the period of when a planet orbits it's star. The alien is from a planet that orbits it's star from a distance of 25,268,817 miles. This makes one Earth year equal to 3.72 Alien years.

[k-man]

A year is determined by how many times a planet orbits a star. The farmer and the alien are from different planets

A year is determined by the period of when a planet orbits it's star. The alien is from a planet that orbits it's star from a distance of 25,268,817 miles. This makes one Earth year equal to 3.72 Alien years.

The OP states that their years are equivalent.

[Guest]

The alien had been traveling at near the speed of light for quite a while, which "relatively" made his years different.

Or possibly they both looked to be about in their late middle-age of life but the aliens typical life span is 300 years.

Or maybe they looked like clones except for that second set of eyeballs, green skin, and a tail?

[Guest]

I was too late and everybody just beat me to answer.

Well, but can anyone tell me how did you get the answer??

I plugged in a computer... you??

Three significant digits of any base is really easy to do since the right most column is the number of ones; the second column is the base, and the 3rd column is the base squared. Using that logic I started with base 3, so 212 = (2*9)+(1*3)+(2*1) = 23 nope too low. Base 4 - 212 = (2*16)+(1*4)+(2*1) = 37, finally I plugged 5 in and got the answer.

[Guest]

The alien had been traveling at near the speed of light for quite a while, which "relatively" made his years different.

Or possibly they both looked to be about in their late middle-age of life but the aliens typical life span is 300 years.

Or maybe they looked like clones except for that second set of eyeballs, green skin, and a tail?

I like you thinking outside the box but the answer was already given using base 5.

[Smith]

The alien had been traveling at near the speed of light for quite a while, which "relatively" made his years different.

Or possibly they both looked to be about in their late middle-age of life but the aliens typical life span is 300 years.

Or maybe they looked like clones except for that second set of eyeballs, green skin, and a tail?

I believe it is the person NOT travelling near the speed of light that ages while the light-speed traveler stays young. But I like your third answer best. Now I have done as your name requests.

[Guest]

I know the answer has already been given, but I'd like to offer a reasoning for the answer...

The human likely uses base 10 due to the number of phalanx groups (fingers & thumb) present on the appendages commonly referred to as 'arms.'

However, the alien uses base 5 due to either an asymmetrical distribution of 'fingers', five 'arms' each with one 'finger' or one 'arm' with five 'fingers.'

I believe it is the person NOT travelling near the speed of light that ages while the light-speed traveler stays young. But I like your third answer best. Now I have done as your name requests.

That is why I have always said that time travel is possible; unfortunately it's always forward in time rather than backward. Also, I think TeaseMe... was trying to say that the alien knew how many years had passed since its birth outside its frame of reference (temporal age; this thought had occurred to me as well) and reported its age based on that number rather than its age within its own frame of reference (physical age). The alien could have easily calculated this value based on frame-time and speed. Edited June 7, 2011 by Egghead

[Guest]

While I believe the base 5 answer was intended and correct, and orbits are outside the OP, I do have another "relative" solution. Space travel near at or beyond the speed of light (Warp 1+x). This would cause the alien to age at a slower rate than the number of years elapsed on their own planetary system. How long this would take to be equal to the farmer's age would depend on the actual speed and the initial age of the alien before leaving for earth. So an exact calculation is not known. But given this is based on the theory of relativity, it is all "relative" anyway. LOL

Edited June 7, 2011 by Magi-Ken

[Guest]

Sometime in the near future, we have a farmer and out of the blue a flaming object falls out of the sky into his field. A creature comes out that has a translation machine that allows him to speak English. They begin conversing until they reach a point where they ask each other their age. The farmer says he is 57 years old. The alien gives him a puzzled look and says that he himself is 212 years old, yet they appear to be about the same age. If the farmer and alien have the same amount of years and their years are equivilant, explain why they give each other two different numbers.

their using two different number system. farmer using 10 digit. alien using 5 digit one..

2 1 2

5^2 5^1 5^0

25 x 2 + 5 + 2 = 57

[Guest]

The problem with the so-called solution.

With the farmer's response of 57, the alien would have known that the farmer's age was not given in base 5.

Neither digit 5 nor 7 are base 5 digits. Thus, he would not have been puzzled, as he would have figured the farmer probably used a base 10 system due to the appearance of similar age.

The puzzle would have been better if the farmer said he was 30, and the alien said he was 132. The farmer's age in base 10 would be 30, and the alien's age in base 4 would also be 30. No digit is greater than used in the base 4 system, thus it would be more possible that the alien could have been confused.

Edited June 7, 2011 by Dej Mar

[Guest]

The problem with the so-called solution.

With the farmer's response of 57, the alien would have known that the farmer's age was not given in base 5.

Neither digit 5 nor 7 are base 5 digits. Thus, he would not have been puzzled, as he would have figured the farmer probably used a base 10 system due to the appearance of similar age.

The puzzle would have been better if the farmer said he was 30, and the alien said he was 132. The farmer's age in base 10 would be 30, and the alien's age given in base 4 is equivalent to the base 10 age of 30. No digit is greater than used in the base 4 system, thus it would be more possible that the alien could have been confused.

[Guest]

The alien's world uses numbers to the base 5, not to base 10, so 57 here is 212 there..

[Guest]

the equivalent "adult" ages using digits of the base 5 system would be:

X₅ __ X₁₀ ... X₅ __ X₁₀... X₅ ___ X₁₀

40 = 20 ... 110 = 30 ... 130 = 40

41 = 21 ... 111 = 31 ... 131 = 41

42 = 22 ... 112 = 32 ... 132 = 42

43 = 23 ... 113 = 33 ... 133 = 43

44 = 24 ... 114 = 34 ... 134 = 44

Besides the few teen and preteen ages not listed, only ages greater or equal to 100 in base 10 could also satisfy the condition of using only digits used in the base 5 system. The age 57 should not have confused the alien visitor, yet these ages may have.

Edited June 8, 2011 by Dej Mar

[Guest]

the equivalent "adult" ages using digits of the base 5 system would be:

X₅ __ X₁₀ ... X₅ __ X₁₀... X₅ ___ X₁₀

40 = 20 ... 110 = 30 ... 130 = 40

41 = 21 ... 111 = 31 ... 131 = 41

42 = 22 ... 112 = 32 ... 132 = 42

43 = 23 ... 113 = 33 ... 133 = 43

44 = 24 ... 114 = 34 ... 134 = 44

Besides the few teen and preteen ages not listed, only ages greater or equal to 100 in base 10 could also satisfy the condition of using only digits used in the base 5 system. The age 57 should not have confused the alien visitor, yet these ages may have.

The alien was confused for two reasons: first, if they were roughly the same age, the number given would not translate into an age that seemed to correspond, and secondly, it is impossible to have 57 in base 5; neither the five and seven digits exist in base 5

[Guest]

The alien was confused for two reasons: first, if they were roughly the same age, the number given would not translate into an age that seemed to correspond, and secondly, it is impossible to have 57 in base 5; neither the five and seven digits exist in base 5

How does 57₁₀ not correspond to 212₅?

As you said, it is impossible to have the number 57 in base 5. (Though, as you should agree, it is not impossible that the value can be represented.) Thus, the alien should not have been confused -- lest the translation machine failed, or his ability to tranverse space did not require an understanding of simple math. (The latter would confuse anyone if such were the case, because it was in part from travelling great distances that higher forms of mathematics were developed).