# Who Married Whom and When?

Louis Thépault offers this puzzle in his book Le chat à six pattes et autres casse-tête : 100 petits problèmes de mathématiques très amusants.

Four men, former classmates, met in a restaurant, each accompanied by his wife. Here’s what we know about these eight people:

1. Alexandre and his wife were born in the same year, both on Mondays. In the year of their wedding Alexandre’s birthday fell on a Friday, and his wife’s on a Thursday.

2. Noëlle, who was given that name because she was born on the 25th of December, is older than her husband.

3. Clara was born in 1982, and her husband was born one January morning.

4. Justine arranged her wedding to fall on the day prior to her birthday, and Dominique vice versa: the wedding on the next day after the birthday; moreover, exactly six days passed between these two weddings: Justine’s was on a Friday and Dominique’s on the next Thursday.

5. Claude, Nicolas’ wife, and Frédéric were born in the same year on Fridays the 13th, Frédéric being the youngest.

6. No two people share a birthday.

Who married whom? Whose wedding was on the 12th of May, 2005, the day before their birthday? Name the exact date of Clara’s wedding.

Classmates means the ages of all eight people don’t vary greatly. Each of the four men was married exactly once to exactly one of the four women, nobody changed their sex/gender etc. All other confusing things are confusing on purpose :-)

• I'm assuming "year" means calendar year. Is that not correct? – Chris Sunami supports Monica Oct 23 '20 at 16:17
• @ChrisSunamisupportsMonica Well yes, the usual Gregorian year, what else could it be? – Roman Odaisky Oct 23 '20 at 16:35
• I thought maybe it meant "within a span of 365 days." If this isn't playing off ambiguity in the term "year" then I'm with @HRogers, none of the ladies can be Alex's bride. – Chris Sunami supports Monica Oct 23 '20 at 18:00
• Having gone and looked up the book referenced, I can confirm that the puzzle does have a valid solution as stated. It requires a good deal of lateral thinking though. I'll post the full answer in a couple weeks if nobody has cracked it by then. – H Rogers Oct 23 '20 at 18:33
• @HRogers It requires absolutely no lateral thinking. What it requires is being very careful with the assumptions. – Roman Odaisky Oct 23 '20 at 22:01

I believe the twist here is that:

Dominique was born on Dec 31st, or Justine was born on Jan 1st.

Why do we need the twist?

It's not too hard to rule out everyone else as being Alexandre's wife. Nicolas is definitely a man, and Claude and Frederic (likely men anyway) were born on Fridays. Noelle being older than her husband doesn't fit with being born in the same year, both on Mondays. Clara being born in 1982 means if she was Alexandre's wife they'd have had to be married in a leap year and he couldn't have been born in January.

From there

Consider Dominique being born on Dec 31st. Then her wedding was on a Thursday, January 1st. Alexandre's birthday could be any Friday in January or February, and then Dominique's birthday would be Thursday, Dec 31st of that year. This requires that they were born on a leap year and married in a non-leap year. Because Clara was born in 1982, Dominique and Alexandre must've been born in either 1980 or 1984 to satisfy the ages not varying greatly. Dec 31st 1980 was a Wednesday, but Dec 31st, 1984 was a Monday. Being born in 1984, they could have married in either 2009 or 2015, as those are non-leap years with Dec 31st falling on a Thursday.

Now consider Justine being born on Jan 1st. Then her wedding was Friday, Dec 31st, and her birthday was Saturday Jan 1st of the next year. So Alexandre and Justine must have been married on a leap year, and Justine's birthday in the year of their wedding was Thursday Jan 1st. However, if you look at Jan 1sts between 1978 and 1986 you'll find that only 1979 had Jan 1st as a Monday. They could have then have been married in 2004, which is a leap year in which Jan 1st was a Thursday.

Now that we have some possibilities established for that person, let's move on to another one.

Let's figure out who Nicolas' wife is. His wife was born on a Friday 13th, so Noelle, Justine, and Dominique are out. The last three people are Claude, Frederic, and Clara. Clue five appears to state that three people were born on three different Friday 13ths in a single year. However, in 1982, when Clara was born, there was only one Friday 13th. So the clue should instead be interpreted as saying "Claude, who is Nicolas' wife, and Frederick..." This results in the women being Noelle, Justine, Clara, and Claude, which also explains why the wording in clue four is so careful to not use a pronoun for Dominique.

We now know who is married to whom:

Alexandre is married to Justine. They were born in 1979, and married on December 31st 2004. Nicolas is married to Claude. Clara married Dominique on January 6th, 2005 - the only Friday, Jan 13ths near 1979 were in 1978 and 1984, so to be born in January Frederic would either need to be about 5 years younger (not classmates) or the oldest. This leaves Frederic and Noelle being married.

As for the May 12th, 2005 wedding

We don't yet know when Nicolas and Claude or Frederic and Noelle were married. From Wikipedia we can see that when May 13th is a Friday it is the only one in the year, so neither Claude nor Frederic were born in May. This leaves Nicolas as the only possibility, so Nicolas and Claude were married on May 12th, 2005 before Nicolas' birthday the next day.

When was Clara's wedding?

January 6th, 2005

• This contradicts the first part of statement 4 unfortunately – Roman Odaisky Oct 27 '20 at 14:46
• This is for sure a breakthrough though! If you take a good look at Joe Ferndz's answer you probably have enough to solve it. – H Rogers Oct 27 '20 at 14:49
• @RomanOdaisky I was thinking there was some problem (especially with how it resulted in the question about the May wedding and Clara's wedding date being redundant), but I was already up too late to bother going through and double checking my work. Did I get it this time? – Rob Watts Oct 27 '20 at 17:56
• @RobWatts congrats, you should probably edit the first part of your response to reflect the final answer. – H Rogers Oct 27 '20 at 20:46

Edit: See comment above. There is a correct solution to the puzzle. Leaving my original (incomplete, incorrect) response for reference.

I may be wrong, but it appears that this puzzle has no correct solution. The easiest way to demonstrate this is to prove that Alexandre cannot be married to any of the four women.

Noelle: Noelle is born on December 25th and is older than her husband. Since Alexandre and his wife were both born on Mondays in the same year, and there is no Monday that comes in a given year following Monday December 25th, Alexandre and Noelle cannot be married.

Justine and Dominique: In the year of Alexandre's wedding his wife's birthday falls on a Thursday, however in the year of Justine's wedding Justine's birthday falls on a Saturday (day after her wedding) and in the year of Dominique's wedding Dominique's birthday falls on a Wednesday (day before her wedding). Therefore, Alexandre cannot be married to either Justine or Dominique.

Clara: The only way for two given dates to land on the same day of the week in one year and a different day of the week in another year (as Alexandre and his wife's birthdays are in their years of birth/marriage) is for one of the years in question to be a leap year. The dates in question must also straddle the end of February. Since 1982 is not a leap year, then the only option is that Clara and Alexandre got married in a leap year. If Clara's birthday came before the leap day and Alexandre's birthday came after, then it would be possible for Alexandre's birthday to be on Friday and Clara's to be on Thursday in their wedding year. However, we are told that Clara's husband was born in January, therefore it is not possible for their birthdays to fall on the given days of the week in their wedding year. Alexandre cannot be married to Clara.

It's possible there's some obscure thing about a day of the week vanishing somewhere in the 80s that I'm not aware of, but barring that the puzzle appears impossible. Or alternatively there's some small mistake in the phrasing (maybe Alexandre's birthday was on Thursday in his wedding year and his wife's was on Friday?).

• No, this apparent contradiction does not follow from the statement of the puzzle. – Roman Odaisky Oct 23 '20 at 14:24
• Any chance you could give a hint as to where I've made a mistake? – H Rogers Oct 23 '20 at 14:53
• I think you got Justine and Dominique's birthdays mixed up with their wedding days ... the wedding on the next day after the birthday; moreover, exactly six days passed between these two weddings: Justine’s was on a Friday and Dominique’s on the next Thursday. This is talking about their wedding days not their birth days. Thats my understanding. So Justine’s birthday on her wedding is Thursday. I paired Alexandre and Justine as husband and wife. The rest I am working thru. – Joe Ferndz Oct 23 '20 at 15:21
• @JoeFerndz The six days in question: Friday, Justine’s wedding; Saturday, Justine’s birthday; Sunday; Monday; Wednesday, Dominique’s birthday; Thursday, Dominique’s wedding. – Roman Odaisky Oct 23 '20 at 15:39
• @RomanOdaisky, you are right. I got mixed up. I did the reverse. Instead of using Saturday, I did Thursday. One day prior to the birthday got mixed up with wedding day. So Justine is not Alexandra's wife. Got it. – Joe Ferndz Oct 23 '20 at 17:02

Based on all the analysis done so far, below are the answers. I am unable to point out Clara's wedding date but I know it is sometime in the 2000+ as shown below:

Dominique: Born 11th May 1983 Wednesday; Wedding 12th May 2005 Thursday
Justine : Female: Born 7th May 1983 Saturday; Wedding 6th May 2005 Friday
Frédéric : Male: Born 13th July 1984 Friday; youngest of all; Wife: Noëlle
Noëlle : Female: Born 25th Dec 1983 Sunday; Husband: Frédéric
Alexandre : Male : Born Jan 1982 Monday; Wife: Clara
Clara is Alexandre's wife; Alexandre born Jan 1982; Clara born between Mar and Dec 1982. They were married in 2007
Claude : Female : Born Jan 13th 1984 or Apr 13th 1984; Friday; Husband: Nicolas

Here are some observations that helped me arrive at above conclusions:

Females:
Noëlle [because of statement #2]
Clara [because of statement #3]
Justine [because of statement #4]
Dominique [potentially female; sometimes can be referred to males]
Claude [potentially female; a common French name given to males]

Males:
Alexandre [because of statement #1: reference to his wife]
Nicolas [because of statement #5: reference to his wife]
Frédéric [because we already have 4 females identified above]
Dominique [if Claude is female; need to figure this out]
Claude [potentially male; it is a common French name given to males]

Claire
Female
Born in 1982
1982 has only one Friday the 13th; need min two Friday the 13th [because of statement #5]
Not born on Friday 13th. Therefore not Nicolas' wife who was born Friday 13th Husband: born Jan

Noëlle
Female
born on 25th December
Older than husband
Not Nicolas' wife [because of statement #5; not born Friday 13th]
Potentially wife of Frédéric (as Frédéric is younger than Claude and Nicolas' wife)
Not Alexandre's wife as Dec 25th does not fall on Monday between 1979 thru 1988
Dec 25th 1978 is a Monday (this will make Noëlle older than all others in the group)

Dominique
Birthday on Wednesday
Wedding on Thursday
Wedding day is 12th May 2005 a Thursday
Born on 11th May 1983 Wednesday
Satisfies Wednesday [statement # 4] for both 11th May 2005 and 11th May 1983

Justine
Female
Wedding on Friday
Birthday on Saturday
Not Alexandre's wife [because of statement #1 and 4]
Wedding day is 6th May 2005 is Friday [because of statement #4 and conclusion from Dominique]
Born on 7th May 1983 Saturday
Satisfies Saturday [statement # 4] for both 7th May 2005 and 7th May 1983

Alexandre
male
Born on Monday
Wedding Year; birthday on Friday
Wife: Born on Monday
Wife: Wedding Year: birthday on Thursday
Wife is not Claude or Frédéric as they are born Friday 13th [because of statement #5]
Wife is not Justine as 7th May 1983 is Saturday [as explained earlier and because of statement #1]
Wife is not Dominique as 12th May 1983 is Wednesday [as explained earlier and because of statement #1]
Wife is not Noëlle. Dec 25h Dec is last week of the year; Noëlle has to be elder than Alexandre; However, Alexandre and Noëlle should be born in the same year which is not possible [because of statements #1 and #2]
Wife is not Nicolas (male) or Frédéric (male + born on Friday 13th)
Claire was born in 1982. For Alexandre and Claire to have the same birth day (Monday) and still have their birthday on different days on their wedding day, they should have got married 25 years later (due to Solar Cycle calendar event.
If you are born in 1982 and married in 2007, your birthday will match statement #1. Alexandra was born on Jan (4th or 11th or 18 or 25th) 1982 [per statement #1 and #3] and Clara was born in between March and Dec 1982 [because of statement #1 and #3]. In 2007, their birthdays fall on Friday and Thursday due to 28 year solar cycle calendar (leap years occur every 4 years and there are 7 possible days to start a leap year resulting in switch in date every 28 years).

• This contradicts statement 1 because 1982-01-04 and 1982-03-01 are both Mondays and the same dates in 2007 are both Thursdays. – Roman Odaisky Oct 24 '20 at 11:34
• @Roman, yes you are correct. While I started Alexandre with Jan 1982, i looked at 1980. Need to go back and redo some of the details. – Joe Ferndz Oct 24 '20 at 16:12
• What is the 25 year "Solar Cycle calendar event" you've mentioned? In any case, Alexandre and Clara can't be born in 1982 and married in 2007 - all days that were Mondays in 1982 were Thursdays in 2007. – Rob Watts Oct 26 '20 at 16:41
• Yes agreed. I need to remove that section. Solar Cycle calendar is a cycle that shows calendar resets every 28 years. 7 days x 4 year leep year cycle. – Joe Ferndz Oct 26 '20 at 18:28