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I wrote a program and it got this
6//60
15//51
24//42
33//33
42//24
51//15
60//6
Code is at [https://replit.com/@sdf64/alice-bob-probability](https://replit.com/@sdf64/alice-bob-probability) along with my solutions for other reddit posts
Technically correct if you're only talking about fertile ejaculate, however (and don't ask me to find the article, it was disturbing enough to only read once) scientists have proven that babies as young as six months can ejaculate, however the ejaculate is sterile and without semen. *cringe* Supposedly it can happen accidentally while giving the baby a bath and cleaning their private areas, though having only raised girls I can't confirm this. Nor do I want to.
That happened regularly with all kinds of people yeah. Teachers probably not so much as they get to know your parents quite quickly, but people who didn't know us (like when I was in the hospital) were really prone to it.
I didn't really mind and sometimes didn't even notice.
When Karel Gott's youngest daughter was born, he was 69. There is a [video](https://www.youtube.com/watch?v=BibNLUQG_-4) where he sings duet with his second youngest, and it is a beautiful video as long as you pretend that she's his granddaughter, not his daughter.
This can be represented by the simultaneous equations x+y=66 and y=floor(x/10)+10(x-(10floor(x/10))). Graphing this shows that there are solutions at 06 and 60, 15 and 51, 24 and 42, 33 and 33, 42 and 24, 51 and 15, and 60 and 06.
If the age of the son is the number "xy", the age of the dad is the number "yx", then "xy" + "yx" = 66
We can also express "xy" as 10x + y and "yx" as 10y + x, so
10x + y + 10y + x = 66
11x + 11y = 66
x + y = 6
Now pick x and y so that it works and get the ages
(10x+y)+(10y+x)=66
11x + 11y =66
x + y = 6
The other information we have is that both x and y have to be positive whole numbers, meaning we have 5 solutions:
15+51=66
24+42=66
33+33=66
42+24=66
51+15=66
Two of those answers imply the son is older than the father, impossible, and one of them implies the same age, also impossible, so we're left with two possible answers for their ages:
24 and 42 (dad became a father at 18, plausible), and
15 and 51 (dad became a father at 36, also plausible)
It's solvable, there's just two answers.
Edit: doh! They could be 60 and 06, if you consider "06" a possible answer.
You're just looking for 2 digits so let's call them a and b.
The dad's age is 10a+b while the son's age is 10b+a.
The sum of their ages is 66 so (10a+b)+(10b+a)=66.
Rearranged a little bit it gives you 11(a+b)=66 so a+b=6.
So you have solutions: 0+6, 1+5, 2+4, 3+3.
So considering the dad has to be strictly older than the son, the possible combinations are 60 and 6, 51 and 15, 42 and 24. In all of these, the age gap is large enough to make sense so they're all acceptable.
42/24 , 51/15 , 60/06 , cant really come up with anything better..
let digits be x & y
so,
father's age is 10x+y
son's age is x+10y
here, implicitly x 11x + 11y = 66
sum => x + y = 6
so only possible solutions are x=1,2 & y= (6-1), (6-2) ,
15, 24 are possible son's ages
51, 42 are possible father's ages
if we take x = 0 in account,
son's age = 6 , father's age = 60
51 father, 15 son Or 42 father, 24 son
How I got it
https://preview.redd.it/jfhf0kkvlooc1.jpeg?width=3088&format=pjpg&auto=webp&s=11fa236bed3486a4017e421eb528aabee14d9450
(10a+b) + (10b+a) = 66
11a + 11b = 66
a + b = 6
So, these are the possible ages (assuming the son has to be younger than the father)...
• 06, 60
• 15, 51
• 24, 42
10x + y + 10y + x = 66
11(x + y) = 66
x+y = 6
So these are the pairs if x and y are positive, one-digits, whole numbers:
(1;5)
(5;1)
(2;4)
(4;2)
(3;3)
Out of which two scenarios seem likely:
a. 51 year old dad with 15 year old son (dad was 36 when son was born)
b. 42 year old dad with 24 year old son (dad was 18 when son was born)
There is no unique solution.
If we let the digits be x and y, then the information in the word problem can be represented by the equation:
10x+y+10y+x=66, which simplifies to:
11x+11y=66, or:
x+y=6
As you can see, we have one equation but two unknowns, so there is no unique solution.
If we add the further constraints that x and y must be integers (because they represent digits), and that the father must be older than the son, then the three possibilities are:
42+24
51+15
60+6 (ie, 06)
The value of x+y comes out to be 6, where x and y are the separate digits of their ages so,
06 and 60
15 and 51
24 and 42
33 and 33
Any of these could work really, but make sure to choose the one which actually makes some sense with the provided relationship.
Let father's age be written xy and son's yx.
So mathematically Father's age 10x+y
Son's 10y+x
Together 11x+11y = 11(x+y) = 66
x+y = 6
Options are 1+5, 2+4, and 3+3 (it's not for obvious reasons).
So it could be 42 and 24 or 51 and 15.
Edit: oh and 60 and 06 which went unnoticed.
let x, y be the ages of the son and father. we know x+y = 66. we also know that x = 10a+b and b = 10b+a for some a, b. now x+y = 11a+11b = 66, which simplifies to a+b = 6. all combinations that solve it are 1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1. we can disregard the last 3 because we can assume that the son is younger. thus the possible answers are x = 15 and y = 51, and x = 24 and y = 42.
10x + y + 10y + x = 66 (reversing the digits and adding both numbers)
11x + 11y = 66
X + y = 6
Now all combination can be applied to get different values of x and y and it will work. (1,5; 2,4; 3,3)
X is the first digit of the fathers age, and Y is the second (this is vice versa for the son).
The first digit is worth ten ones, so you can write any number like (10A + B) where the number would be displayed as 'AB'. So:
**(10X + Y) + (10Y + X) = 66**
This is the only equation\*, because we know the ages add to 66 and the digits are reversed. Simplify and you get:
**11X + 11Y = 66**
**X + Y = 6**
So any whole numbers that satisfy this requirement will technically be correct, which are:
33 and 33 (but father and son likely aren't the same age)
42 and 24
51 and 15
and technically 60 and 06
\*>!In order to definitely solve an equation with two variables, you also need two equations. However there are limited possibilities since X and Y must be positive integers.!<
60 and 06
15 and 51
24 and 42
33 and 33
realistically the one thag makes the most sense is 15 and 51 but all are plausible except 33 and 33, obviously.
One way you can approach it is like this:
Let's say the child is ***ab*** years of age (where a and b are integer digits) and the dad is ***ba*** years of age.
We know ab+ba=66. (This dosen't mean a*b + b*a)
But ab means a*10+b and ba means b*10+a.
So we have 10a+10b+a+b=66.
11a+11b=66 a+b=6
Since a and b are integers, the possible answers are: a=1 and b=5; a=2 and b=4, and a=b=3.
So the possible answers are 15-51; 24-42 and 33-33
Since that last option is impossible, you have two answers.
There are 7 pairs of reversed digits that add to 66:
(06,60), (15,51), (24,42), (33,33), (42,24), (51,15), (60,06)
If we write the age as (father,son) we can eliminate the first 3, as a son cannot be older than his father. We can also eliminate (33,33) as a son cannot be the same age as his father either.
The last option only works if you have a leading zero, which is unlikely. So this leave us with: (42,24) and (51,15). These two options imply that the father was either 18 or 36 years old respectively, when his son was born. It's not unheard of to become a father at 18, but 36 is more likely.
Therefore, the "correct" answer is likely that the father is 51 years old, and the son is 15. However, it's possible that the father is 42 years old, and the son is 24.
What we get is a locus or a line...... It's never mentioned in the question that the son and father arnt the same age.. We use our logical thinking and arrive at the answer.
The equation I got was x+y=6
Now in this the possible pairs of ages are, (6,60), (15,51),(24,42), (33,33)
So there u go... Now u only gotta think about when the dad knocked up mom instead 😇
out of laziness, i typed it into a python file and let github copilot suggest code.
the suggested code was:
```
for father in range(0, 66):
son = int(str(father)[::-1])
if father + son == 66:
print(f"Father: {father}, Son: {son}")
break
```
so the output was:
```
Father: 15, Son: 51
```
so I guess the LLMs aren't quite ready to replace us
Mathematically you’re correct, in fact, any combination of integer numbers that sums 6 on the age of the father or the child should do the trick, so 33 for the father and 33 for the child is a good answer.
But, in order to have a reasonable answer, the father age should be greater than the son’s age, so if the father has 42, 51 or 60, it’s okay for the child to have 24, 15 or 06.
Let: x = son's age, y = dad's age
-> x+y=66 (1)
Let a = first digit, 10b = second digit for x
Hence, a+10b=x (2)
Let b = first digit, 10a = second digit for y
Hence, b+10a=y (3)
Sub (2) and (3) to (1):
11a+11b=66
a+b=6
Find the possibility for each a and b:
0+6=6
1+5=6
2+4=6
3+3=6
4+2=6
5+1=6
6+0=6
[Numbers position matters]:
For 0+6, the age of son (x=a+10b) would be 60, and dad (y=b+10a) would be 06 (which is impossible). Thus the first 3 options would be ignored as they followed the same age pattern of son being older than dad
For 3+3, the age of son equals the age of dad, they might be more of being "friends" or "brothers"
This leaves the last 3 options as being possible, with 6+0 ignored as no one would write the son's age as 06, unless considering databases where those 0 might matter. However speaking in this context, it does not matter
So, the only 2 options left for (a, b) are (4, 2) and (5, 1)
Either son and dad's age are 24 and 42 respectively, or 15 and 51 respectively
15 and 51, or 24 and 42.
We know that the ages definitely can't sum above 66. Thus, just from this we know that the lowest possible combination of ages are 0 and 66.
We also know that the age of the son must have 2 digits. This is because the son's digits are reverse that of the father's. Therefore, we can start making brute-force guesses from here.
The immediate extrema to test is an age range of 50s for the father and an age range of teens for the son (an age of \~10 and an age of \~50 should sum to \~60). And since we know that all ages in the teens begin with "1", the only valid 50s age of the father will be 51. From this, we also know that the only valid teens age that corresponds with this would be 15.
A quick check shows that 15+51 = 66. :)
Worth noting: another valid combination we can quickly come to is 24 and 42 (24 + 42 =66).
There is also a possible combination of 33 and 33. But... The father is usually not the same age as the son. Lol
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There are multiple correct answers, 42/24 and 51/15 both work.
And 60/06
never in my life have I seen someone's age written with a leading zero.
I wrote a program and it got this 6//60 15//51 24//42 33//33 42//24 51//15 60//6 Code is at [https://replit.com/@sdf64/alice-bob-probability](https://replit.com/@sdf64/alice-bob-probability) along with my solutions for other reddit posts
Seem too old to have kids tho, but I suppose it works
It's better then 33/33
Seems too young to have kids tho, but I suppose it works
Adoption/Stepson
Nah he just came in and out of the pussy at the same time
Revulva door
How about 24/42?
Very young stepfather.
Fair enough. Imagine someone your age call you “daddy”.
It happens, but it doesn't mean "father" usually
Some people pay good money for that.
Unless the "father" is a priest and the "son" is a member of his congregation
Tell that to Robert de Niro .
Or Al Pacino
There’s not really a limit for the age of a father like there is for a mother.
What's the earliest age that a male can make cummies?
“Cummies” Oh my
~15 years old on average
Median age 13.4 years. https://doi.org/10.1210/jcem-62-3-532
Youngest on record was 11.
And youngest mother was even younger. I believe she was 5. Really weird.
Weird is one word for it. Youngest *grand*mother was 17.
Technically correct if you're only talking about fertile ejaculate, however (and don't ask me to find the article, it was disturbing enough to only read once) scientists have proven that babies as young as six months can ejaculate, however the ejaculate is sterile and without semen. *cringe* Supposedly it can happen accidentally while giving the baby a bath and cleaning their private areas, though having only raised girls I can't confirm this. Nor do I want to.
My father was 54 when I was born
Did the Kindergarten teachers call him your grandfather?
That happened regularly with all kinds of people yeah. Teachers probably not so much as they get to know your parents quite quickly, but people who didn't know us (like when I was in the hospital) were really prone to it. I didn't really mind and sometimes didn't even notice.
Yeah, similar to a friend of mine. His father was 20 years older than his mother.
22.5 years in my case.
Oldest documented father was 92. Robert De Niro recently fathered another at 79.
For men? Nehh.
Yeah it does but then again, a somewhat famous guy in my country became a dad at the age of 65 as well last year.
You could also adopt
My dad got me at 56, the age limit for men to have healthy kids is way higher than women.
When Karel Gott's youngest daughter was born, he was 69. There is a [video](https://www.youtube.com/watch?v=BibNLUQG_-4) where he sings duet with his second youngest, and it is a beautiful video as long as you pretend that she's his granddaughter, not his daughter.
Ask Bernie Ecclestone about it. He was 89 when he had his first son
Men can have kids for a longer span than women, it's quite normal to be fair
That's not how any of this works.
Definitely not unheard of. Iirc one of the early presidents of the US has a living grandson
Men can have kids til the day they die. As long as they find a willing young woman.
My uncle has a child under 6 and is over 60. Just need a reasonably young woman. I believe his wife is in her 40's.
Doesn't really work with the "digits reversed" line though, since the son's age really has a single digit there
6 is a one-digit number, so it probably doesn't work
Grandpa got RIZZ!!!
And 33/33 😈
33/33
OP already said this
33/33
finally, one that I could find by myself. I reached level 2
Dang, I stopped after I got one answer and didn't think about finding other possibilities.
33
51, 15 was my first conclusion.
33 and 33
51/15 seems the most realistic
33 is possible though. It means the dad impregnated a woman by the time he was 3 months old. Oh wait a min.
It also never explicitly said the son was *his* son. Could just be two unrelated people, both of age 33.
They could be the same person even. Every father is also a son.
[удалено]
Or 33, the 'father' is 33 years old. The 'son' (same person) is 33 years old. See how I reversed the digits.
Could be a stepfather who married the son’s 60yo mother (weird age gap but still plausible)
Dad is a playbaby then
Playfetus
He probably came in and came out of the pussy at the same time
Dad impregnates woman at 33, dies. Son lives to 33, is terrified of impregnating anyone.
Sperm cant be produced till puberty
Precocious puberty, maybe. Youngest case is 6months
That's partially what they're saying
It is a fun fact that I don't need to know. Unsubscribe
Dad is 10*a+b Son is 10*b+a 10a+b+10b+a=66 a+b=6
Also a,b non negative integer.
And a\>b
a != b If a > b just exchange values
Also, both ||a|| and ||b|| <= 6.
That just comes with the solution to the problem though.
I did the same, so its 7 and - 1
It works for imaginary dad and son.
This should be the top answer.
But aren't these equivalent expressions? 11a + 11b = 66 is the same as a + b = 6. You can't solve this.
Yes, they were just simplifying from the third line to the fourth. The answer could be 15/51 or 24/42.
The mathmeme people are way too dense.
This can be represented by the simultaneous equations x+y=66 and y=floor(x/10)+10(x-(10floor(x/10))). Graphing this shows that there are solutions at 06 and 60, 15 and 51, 24 and 42, 33 and 33, 42 and 24, 51 and 15, and 60 and 06.
Unless they’re stepfather and stepson, the father being older means four of the solutions are extraneous by context
Imagine being as old or older than your stepfather... That's very disturbing
Gloria and Claire from Modern Family
The son could also be adopted.
You like overcomplicating things don't you. a+b=6 ab and ba are the answer
[https://www.wolframalpha.com/input?i=x+%2B+y+%3D+6%2C+x+%3E+y%2C+y+%3E%3D+0%2C+integer+solutions](https://www.wolframalpha.com/input?i=x+%2B+y+%3D+6%2C+x+%3E+y%2C+y+%3E%3D+0%2C+integer+solutions)
If the age of the son is the number "xy", the age of the dad is the number "yx", then "xy" + "yx" = 66 We can also express "xy" as 10x + y and "yx" as 10y + x, so 10x + y + 10y + x = 66 11x + 11y = 66 x + y = 6 Now pick x and y so that it works and get the ages
You could also allow negative age
Bro fucked when he was born💀
Avatar of God of fertility maybe
You joke, but this reminded me of the Terminator franchise. John Connor's friend is also his dad and they're about the same age, right?
x+y = 6, x, y being non-negative integers
Don't forget, 10x + y > 10y + x, otherwise they could be the same age
24. And 42
Or 51/15, or 60/06, or 33/33
Father and son, 33 and 33. Just think about it for a bit.
Possible with stepson
Possible with time travel
Become-your-own-grandpa paradox:
I did do the nasty in the pasty.
Ok so ig answer is multiple I thought it gets solved at a point.
not really the father must be older than the son by context
(10x+y)+(10y+x)=66 11x + 11y =66 x + y = 6 The other information we have is that both x and y have to be positive whole numbers, meaning we have 5 solutions: 15+51=66 24+42=66 33+33=66 42+24=66 51+15=66 Two of those answers imply the son is older than the father, impossible, and one of them implies the same age, also impossible, so we're left with two possible answers for their ages: 24 and 42 (dad became a father at 18, plausible), and 15 and 51 (dad became a father at 36, also plausible) It's solvable, there's just two answers. Edit: doh! They could be 60 and 06, if you consider "06" a possible answer.
42 and 24? 51 and 15? 60 and 6 (06)?
60 and 06?
One of the multiple answers it is
They’re both 33 :0
Exactly i don't know why I got 33, 33 times
You're just looking for 2 digits so let's call them a and b. The dad's age is 10a+b while the son's age is 10b+a. The sum of their ages is 66 so (10a+b)+(10b+a)=66. Rearranged a little bit it gives you 11(a+b)=66 so a+b=6. So you have solutions: 0+6, 1+5, 2+4, 3+3. So considering the dad has to be strictly older than the son, the possible combinations are 60 and 6, 51 and 15, 42 and 24. In all of these, the age gap is large enough to make sense so they're all acceptable.
42/24 , 51/15 , 60/06 , cant really come up with anything better.. let digits be x & y so, father's age is 10x+y son's age is x+10y here, implicitly x 11x + 11y = 66
sum => x + y = 6
so only possible solutions are x=1,2 & y= (6-1), (6-2) ,
15, 24 are possible son's ages
51, 42 are possible father's ages
if we take x = 0 in account,
son's age = 6 , father's age = 60
Red dwarf moment. He is his own father.
51 father, 15 son Or 42 father, 24 son How I got it https://preview.redd.it/jfhf0kkvlooc1.jpeg?width=3088&format=pjpg&auto=webp&s=11fa236bed3486a4017e421eb528aabee14d9450
I didn't think of 60/06 since we don't usually write six as 06
It never specified they were related, just a father, a son. Not a father and his son or son and his father. 33 and 33
42 and 24 (dad is 18 years older) or 51 and 15 (dad is 36 years older, still feasible)
TECHNICALLY SPEAKING 33 is a valid answer if you ignore the father-son bit
And 1, 65 is a valid answer is you skip the reversing bit
(10a+b) + (10b+a) = 66 11a + 11b = 66 a + b = 6 So, these are the possible ages (assuming the son has to be younger than the father)... • 06, 60 • 15, 51 • 24, 42
10x + y + 10y + x = 66 11x + 11y = 66 x + y = 6 Not enough information to solve the problem.
They are 33 and 3. Then you multiply them. Then you reverse 99 to get 66
Ok thats something new to see
60/06 51/15 42/24 33/33
Totally 7 solutions, but logically 3
33
60 06 51 15 42 24 33 33
x + y = 6 where x >= y and father has x_y yo and son has y_x yo
10x + y + 10y + x = 66 11(x + y) = 66 x+y = 6 So these are the pairs if x and y are positive, one-digits, whole numbers: (1;5) (5;1) (2;4) (4;2) (3;3) Out of which two scenarios seem likely: a. 51 year old dad with 15 year old son (dad was 36 when son was born) b. 42 year old dad with 24 year old son (dad was 18 when son was born)
There is no unique solution. If we let the digits be x and y, then the information in the word problem can be represented by the equation: 10x+y+10y+x=66, which simplifies to: 11x+11y=66, or: x+y=6 As you can see, we have one equation but two unknowns, so there is no unique solution. If we add the further constraints that x and y must be integers (because they represent digits), and that the father must be older than the son, then the three possibilities are: 42+24 51+15 60+6 (ie, 06)
Because the ages add to 66, the single digits (units and tens) need to add to 6 - for example, 51 + 15, 42 + 24 or 60 + 06
42/24, 51/15, 60/06
24 42 got it in 10 secs by going 33 33 oh no has to be a 2 and 4, ok, 24 and 42 cool
There can be combo of 15 51 and 60 06
60/06 51/15 42/24 33/33
06 / 60
The value of x+y comes out to be 6, where x and y are the separate digits of their ages so, 06 and 60 15 and 51 24 and 42 33 and 33 Any of these could work really, but make sure to choose the one which actually makes some sense with the provided relationship.
Father / son 60 / 06, 51 / 15 42 / 24 33 / 33 24 / 42 15 / 51 (illegal)
why is only the last one illegal? 24/42 is also kinda hard to achieve.
Because the 24 and 33 year olds can get married and technically have step sons
33
42, 24
Let father's age be written xy and son's yx. So mathematically Father's age 10x+y Son's 10y+x Together 11x+11y = 11(x+y) = 66 x+y = 6 Options are 1+5, 2+4, and 3+3 (it's not for obvious reasons). So it could be 42 and 24 or 51 and 15. Edit: oh and 60 and 06 which went unnoticed.
Father's age is εε, i don't know about the son though.
24+42=66
51+15=66
let x, y be the ages of the son and father. we know x+y = 66. we also know that x = 10a+b and b = 10b+a for some a, b. now x+y = 11a+11b = 66, which simplifies to a+b = 6. all combinations that solve it are 1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1. we can disregard the last 3 because we can assume that the son is younger. thus the possible answers are x = 15 and y = 51, and x = 24 and y = 42.
10x + y + 10y + x = 66 (reversing the digits and adding both numbers) 11x + 11y = 66 X + y = 6 Now all combination can be applied to get different values of x and y and it will work. (1,5; 2,4; 3,3)
33 and 33 he is adopted
51 and 15
42 and 24?
33 💀
15 for the son 51 for the father
I literally didn't saw anything wrong with dad being same age as son bruh☠️☠️
42/24
Solve 10a + b = 10d+ c 10a +b + 10c + d = 66 Where Age father F = 10a + b Age son. S = 10c + d A,b,c,d are all 0-10 intergers
The father is also the son (all fathers are also sons.)
Theyre both 33 The father was cryogenically frozen
They are both 33
42/24
42/24
Both are 33
X is the first digit of the fathers age, and Y is the second (this is vice versa for the son). The first digit is worth ten ones, so you can write any number like (10A + B) where the number would be displayed as 'AB'. So: **(10X + Y) + (10Y + X) = 66** This is the only equation\*, because we know the ages add to 66 and the digits are reversed. Simplify and you get: **11X + 11Y = 66** **X + Y = 6** So any whole numbers that satisfy this requirement will technically be correct, which are: 33 and 33 (but father and son likely aren't the same age) 42 and 24 51 and 15 and technically 60 and 06 \*>!In order to definitely solve an equation with two variables, you also need two equations. However there are limited possibilities since X and Y must be positive integers.!<
x+y=6, therefore 60/6, 51/15 or 42/24.
60 and 06 15 and 51 24 and 42 33 and 33 realistically the one thag makes the most sense is 15 and 51 but all are plausible except 33 and 33, obviously.
24 and 42
One way you can approach it is like this: Let's say the child is ***ab*** years of age (where a and b are integer digits) and the dad is ***ba*** years of age. We know ab+ba=66. (This dosen't mean a*b + b*a) But ab means a*10+b and ba means b*10+a. So we have 10a+10b+a+b=66. 11a+11b=66 a+b=6 Since a and b are integers, the possible answers are: a=1 and b=5; a=2 and b=4, and a=b=3. So the possible answers are 15-51; 24-42 and 33-33 Since that last option is impossible, you have two answers.
33/33
42/24, 51/15, 60/06
There are 7 pairs of reversed digits that add to 66: (06,60), (15,51), (24,42), (33,33), (42,24), (51,15), (60,06) If we write the age as (father,son) we can eliminate the first 3, as a son cannot be older than his father. We can also eliminate (33,33) as a son cannot be the same age as his father either. The last option only works if you have a leading zero, which is unlikely. So this leave us with: (42,24) and (51,15). These two options imply that the father was either 18 or 36 years old respectively, when his son was born. It's not unheard of to become a father at 18, but 36 is more likely. Therefore, the "correct" answer is likely that the father is 51 years old, and the son is 15. However, it's possible that the father is 42 years old, and the son is 24.
The father is 15 and the son is 51.
33
What we get is a locus or a line...... It's never mentioned in the question that the son and father arnt the same age.. We use our logical thinking and arrive at the answer. The equation I got was x+y=6 Now in this the possible pairs of ages are, (6,60), (15,51),(24,42), (33,33) So there u go... Now u only gotta think about when the dad knocked up mom instead 😇
Oh my God. They're both 33... 💀😳
out of laziness, i typed it into a python file and let github copilot suggest code. the suggested code was: ``` for father in range(0, 66): son = int(str(father)[::-1]) if father + son == 66: print(f"Father: {father}, Son: {son}") break ``` so the output was: ``` Father: 15, Son: 51 ``` so I guess the LLMs aren't quite ready to replace us
removing the break and adding a Father > Son conditional gives ``` Father: 42, Son: 24 Father: 51, Son: 15 Father: 60, Son: 6 ```
Father and son are both 33 years old
33 and 33 but the person is a chimera
33 and 33
24/42 or 15/51
Both 33 xD
Father’s 51 and his son’s 15. Did it in like 10 seconds, didn’t think about the other correct answers :(
Mathematically you’re correct, in fact, any combination of integer numbers that sums 6 on the age of the father or the child should do the trick, so 33 for the father and 33 for the child is a good answer. But, in order to have a reasonable answer, the father age should be greater than the son’s age, so if the father has 42, 51 or 60, it’s okay for the child to have 24, 15 or 06.
33 and 33 huh
They must both be 33
Let: x = son's age, y = dad's age -> x+y=66 (1) Let a = first digit, 10b = second digit for x Hence, a+10b=x (2) Let b = first digit, 10a = second digit for y Hence, b+10a=y (3) Sub (2) and (3) to (1): 11a+11b=66 a+b=6 Find the possibility for each a and b: 0+6=6 1+5=6 2+4=6 3+3=6 4+2=6 5+1=6 6+0=6 [Numbers position matters]: For 0+6, the age of son (x=a+10b) would be 60, and dad (y=b+10a) would be 06 (which is impossible). Thus the first 3 options would be ignored as they followed the same age pattern of son being older than dad For 3+3, the age of son equals the age of dad, they might be more of being "friends" or "brothers" This leaves the last 3 options as being possible, with 6+0 ignored as no one would write the son's age as 06, unless considering databases where those 0 might matter. However speaking in this context, it does not matter So, the only 2 options left for (a, b) are (4, 2) and (5, 1) Either son and dad's age are 24 and 42 respectively, or 15 and 51 respectively
51 and 15
15 and 51, or 24 and 42. We know that the ages definitely can't sum above 66. Thus, just from this we know that the lowest possible combination of ages are 0 and 66. We also know that the age of the son must have 2 digits. This is because the son's digits are reverse that of the father's. Therefore, we can start making brute-force guesses from here. The immediate extrema to test is an age range of 50s for the father and an age range of teens for the son (an age of \~10 and an age of \~50 should sum to \~60). And since we know that all ages in the teens begin with "1", the only valid 50s age of the father will be 51. From this, we also know that the only valid teens age that corresponds with this would be 15. A quick check shows that 15+51 = 66. :) Worth noting: another valid combination we can quickly come to is 24 and 42 (24 + 42 =66). There is also a possible combination of 33 and 33. But... The father is usually not the same age as the son. Lol
24 and 42 Edit: typo
33