a maths riddle

Hint: you are looking for three integers that multiply to give 36, and you are told that the smallest is unique (e.g. that rules out 3,3,4).

Reply 2

nota bene

What about 1, 4, 9 then? (Or am I missing something?)

Reply 3

RichE

designJ

Hey guys

I just came asross the following riddle along with the answer but I dont understand it. please can someone explain the reasons for the answer.

Cheers

A man bumps into his mathematician friend on the street that he hasn't seen in 5 years. The man asks the mathematician how old his children are. The mathematician, who always replies in riddles said, "I now have three children. The sum of their ages is equal to the number of windows on the building in front of you and the product of their ages equals 36." The friend then says "I need one more piece of information." The mathematician then replies "My youngest child has blue eyes." What are the ages of the mathematicians three children?

Answer, 6, 6 and 1.

Let's say that the ages of the children are x,y,z. One fact we know is that xyz = 36. The list of possibilities are:-

36,1,1 - sum is 38
18,2,1 - sum is 21
9,4,1 - sum is 14
9,2,2 - sum is 13
6,6,1 - sum is 13
6,3,2 - sum is 11

If we weren't in the sum = 13 situation then the guy wouldn't need any further info. So we're in a 9,2,2 or 6,6,1 situation.

I think we're meant to read into the last piece of info that the elder two are twins, rather than the younger two - so that there is indeed a "youngest" and so we're in the 6,6,1 situation.

Reply 4

I think the point is that he hasn't seen his friend in five years, and asks "How old are your CHILDREN?" (i.e. he knows there is more than one). Thus the eldest two must be at least five.

EDIT: Oh right. RichE's point is much better :biggrin:

Reply 5

Using second piece of info (product of ages is 36), the children's ages can be:
1, 1, 36; 1, 2, 18; 1, 3, 12; 1, 4, 9; 1, 6, 6; 2, 2, 9; 2, 3, 6; 3, 3, 4

Using first piece of info (sum is equal to the number of wondows), the totals are:
38, 21, 16, 14, 13, 13, 11, 11

Now, the man must know how many windows there are, so he should be able to work out the ages if the number of windows is 38, 21, 16 or 14. But he can't, so the sum of the ages must be 13 or 11, meaning the children are either 1, 6, 6; 2, 2, 9; 2, 3, 6; or 3, 3, 4

When told the youngest child has blue eyes, it means the youngest is not one of a twin, so 2, 2, 9 and 3, 3, 4 are ruled out. Since 1, 6, 6 and 2, 3, 6 are left, and the man hasn't seen his friend for five years, he would only not know about children 5 years old or less. Presumably he knows the mathematician had two children back then (but didn't know their ages), so can conclude there are two children over the age of 5, so the ages are 1, 6, 6

Reply 6

nota bene

James Gurung

I think the point is that he hasn't seen his friend in five years, and asks "How old are your CHILDREN?" (i.e. he knows there is more than one). Thus the eldest two must be at least five.

You're right :biggrin:

*feels stupid, runs away to continue on essay*

Reply 7

insparato

James Gurung

I think the point is that he hasn't seen his friend in five years, and asks "How old are your CHILDREN?" (i.e. he knows there is more than one). Thus the eldest two must be at least five.

EDIT: Oh right. RichE's point is much better :biggrin:

I was thinking that :smile:

.

Reply 8

I'm not sure about that. If the man knows the mathematician had two children over the age of five, and their sum was 13 (as he can count the windows), and product was 36, surely that would be enough information?

Actually, all he needed to know was that 2 kids were older than 5, and the product is 36 :s-smilie:

Unless I'm missing a way of splitting up 36...

Reply 9

Here's another:

You walk 1km South, then 1km due East and finally 1km North. This brings you back to where you started. Where is this possible?

North Pole :p:

Lol you're missing solutions! :biggrin:

Reply 12

For your riddle, or designJ's? :s-smilie:

Reply 13

Mine. You could be at the North Pole, but there are lots of other places you could start :wink:

Reply 14

ukgea

Any point with latitude v satisfying v < 0 (positive being north) and for which there exists a positive integer n such that 2R*n*pi*cos (v - 1km/R) = 1 km (where R is the radius of the earth, assuming of course the earth is a perfect sphere).

I always used to hate it when you were given these kinds of riddles on iq-style tests and they always missed out all the southern hemisphere solutions. :mad:

Reply 15

That's clever. You mean you go south towards south pole, walk around it a whole number of times until starting point is directly 1km north of you again?

Reply 16

Yep

. I think the problem was designed to point out the problem with solution "by inspection". I'm very surprised it was used wrongly in IQ tests!

Reply 17

-42-

1

This is a bit of a, well, odd, riddle, you might hate me when I tell you the answer but how would you describe this sequence:

H J L M N O

Reply 18

ukgea

Another one:

"ukgea, Trangulor and James are standing together in a great hall called The Student Room.

Lacking anything better to do, ukgea suddenly announces: 'I will now choose two positive integers, not necessarily distinct, and I am going to tell Trangulor their sum and James their product.' And so he whispers the sum of the two numbers to Trangulor and the product to James. 'Now, tell me, which two integers did choose?'

James is the first to reply. 'I don't know' he says, and the expression on his face was revealing that he indeed was telling the truth.

Trangulor now replies 'I don't know either', and sighs heavily.

The room now fell silent. But James is staring at the ceiling in pondrance. After a while, he looks down again, shakes his head, and says: 'I still don't know'.

Intrigued, Trangulor now falls deep into thought. 'Nope' he says. 'Neither do I'.

Then suddenly, James exclaims: 'Eureka! I got it!' and Trangulor then smiles: 'Oh, now I know too!'"

So, which are the two integers?

(It shall of course be assumed that both James and Trangulor are infitely intelligent, have infinitely good memory, etc etc... :wink:

)

Reply 19