2 oldest are twin

[jasen]

2 mathematicians meet at their school reunion.
mat 1 : Hey old friend, I heard you have 4 child, How old are they?
mat 2 : Sum of their multiplicative inverse is 1, and sum of their age is your sister age.
mat 1 : But, I still don't know their ages.
mat 2 : 2 oldest are twin.
mat 1 : ok, I know know.

Edited January 12, 2016 by jasen

[DejMar]

Spoiler

Given that the first mathematician was unable to know the ages of the four children, the sum of the ages occurs multiple times for different sets of integer ages where the sum of the reciprocals equals the multiplicative identity. This only occurs where the sum is 22 (which must be the age of the first mathematician's sister). These values are: (8,8,4,2), (6,6,6,2), (12,4,3,3).
Given the oldest two are twins reduces this to two possibilities:  (8,8,4,2) and (6,6,6,2). The first set is likely the intended answer, though the second can not be dismissed without consideration. (It is a fact that a child can be born less than a year after an older sibling, thus for a short period they can have the same age). Still, considering that a single solution is sought, the ages themselves are to be considered the compose the twins (as opposed to the children), and thus (8,8,4,2) would be the answer.

 

[jasen]

16 hours ago, DejMar said:

  Reveal hidden contents

Given that the first mathematician was unable to know the ages of the four children, the sum of the ages occurs multiple times for different sets of integer ages where the sum of the reciprocals equals the multiplicative identity. This only occurs where the sum is 22 (which must be the age of the first mathematician's sister). These values are: (8,8,4,2), (6,6,6,2), (12,4,3,3).
Given the oldest two are twins reduces this to two possibilities:  (8,8,4,2) and (6,6,6,2). The first set is likely the intended answer, though the second can not be dismissed without consideration. (It is a fact that a child can be born less than a year after an older sibling, thus for a short period they can have the same age). Still, considering that a single solution is sought, the ages themselves are to be considered the compose the twins (as opposed to the children), and thus (8,8,4,2) would be the answer.

 

Right Answer, but you make a bit miscalculation. sum of 6,6,6,2 is 20, not 22.

Spoiler

1^st Clue  : Sum of their multiplicative inverse is 1

All age possibility are

4th child	3rd child	2nd child	1st child	sum ages
2	3	7	42	54
2	3	8	24	37
2	3	9	18	32
2	3	10	15	30
2	3	12	12	29
2	4	5	20	31
2	4	6	12	24
2	4	8	8	22
2	5	5	10	22
2	6	6	6	20
3	3	4	12	22
3	3	6	6	18
3	4	4	6	17
4	4	4	4	16

2^nd Clue  : Sum of their age is your sister age

Because “mat 1” said that knowing the total (from the age of her sister) did not help, we know that knowing the sum of the ages does not give a definitive answer; thus, there must be more than one solution with the same total.

Only three sets of possible ages add up to the same totals:

2	4	8	8	22
2	5	5	10	22
3	3	4	12	22

3^rd clue : 2 oldest are twin

“mat 2” concludes that the correct solution is 8,8,4,2.

 

 

 

Edited January 13, 2016 by jasen

[DejMar]

I am guessing I visually transposed one pair of rows in the spreadsheet. 6+6+6+2 does equal 20. Perhaps I was entranced by that twenty-year-old, and took my eyes off the mathematician's sister.