## June 08, 2009

### Maths Challenge #8 – Family Occasion

'It was a wonderful party,' said Lucilla to her friend Harriet.
'Who was there?'
'Well - there was one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law.'
'Wow! Twenty-three people!'
'No, it was less than that. A lot less.'

What is the smallest size of party that is consistent with Lucilla's description?

### 10 comments by 3 or more people

1. Seven, two grandparents, one son of the grandparents and his wife who are the mother and father of three children (two girls and a boy). I got this too quickly. What have I done wrong???

08 Jun 2009, 13:09

2. #### Sebastien Dutrieu

I also found 7, same way too.

08 Jun 2009, 13:30

3. #### James Turner

Any 1 male can be a grandfather, father, child, son, grandchild, brother, and father in law. And similarly with females.

The problem doesn’t state, for example, that the father-in-law’s son-in-law was as the party. So a female can fulfil the daughter-in-law requirement and the mother-in-law requirement.

Thus, the minimum number of people is 4 because of the “four children”
As you need 2 father and 2 mothers, there must be 2 males and 2 females at the party.

So the total is 4.

08 Jun 2009, 14:55

4. #### sUSAN

It’s interesting (and quite shocking) when you think of all the roles you play in life. In my case I’m a mother, daughter, grandaughter, daughter-in-law, cousin, auntie, sister, bitch, slag and entrepeneur.

08 Jun 2009, 16:27

5. #### Eleanor Lovell

The answer is 7 – two small girls and one boy, their father and mother, and their father’s father and mother.

09 Jun 2009, 13:31

6. #### Steve Rumsby

I think that’s right if you need both sides of each relationship in the party, but the question didn’t say that. I’m a son and a father whether or not my dad and kids are in the room with me. On that basis I agree with others above that you can do it with just 4 people.

09 Jun 2009, 14:01

7. #### Iain Wallace

Disagree – James’ answer is correct. The question doesn’t state that, for example the relation that makes the person a child is present at the party, thus the grandparents can count as children as they are the children of their own parents.

09 Jun 2009, 14:02

8. I think the problem is that it says ‘3 grandchildren’. from this you can infer that their grandparents must be present. if you do not make this inference, as is the case if you limit it to 4 people, then you would have 4 grandchildren (as everybody is a grandchild of somebody) and not 3.

09 Jun 2009, 14:23

9. #### Steve Rumsby

Unless you only called somebody a grandchild if they had a grandparent still living…

The fundamental problem here seems to be that the problem is under-specified, leaving us to make some assumptions before we can come up with an answer. Different assumptions produce different answers.

09 Jun 2009, 14:38

10. #### Accessories

Nice blog dude..
Actually i hate maths because its so logical subject..

13 Jun 2009, 10:00

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Warwick Challenges are mini academic challenges from University of Warwick professors, set via the micro-blogging service Twitter (and also via this blog).
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