Det var to matematikere som møttes på en konferanse i Nice et år, de het Nils og Magne. De gikk på samme universitet for flere år siden, og de har ikke treftes siden da. Etter denne konferansen treftes de i foajen i hotellet. De pratet sammen, og etter hvert spurte Nils om hvor mange barn Magne hadde. Han svarte at han hadde tre barn. Nils ville også vite hvor gammel de tre var, men siden begge var matematikere svarte Magne:
- Hvis du plusser opp alderen til barna mine så er tallet 13.
- Jeg la også merke til at hvis du ganger alderen til mine tre barn, så vil du få det nummeret du har på rommet ditt i dette hotellet.
De gikk hvert til sitt, men Nils var enda ikke helt fornøyd. Da de treftes igjen så sa Nils:
- "Jeg må ha en opplysning til for å vite alderen på de tre ungene dine", sa han.
- "Ja, det stemmer jo! Mitt eldste barn er født i New York", svare Magne.
- "Ahh, da vet jeg alderen på barna dine", svarte Nils.
Hvordan kunne Nils finne ut alderen på de tre ved hjelp av de opplysningene som er gitt?
I am not sure if the Google translation from Norwegian to English is good enough for this but lets see.
There were two mathematicians who met at a conference in Nice one year, they called Nils and Magne.
They went to the same university several years ago, and they have not been met since then. After this conference, they meet in the foyer of the hotel. They talked together, and eventually Nils asked about how many children Magne had. He replied that he had three children. Nils also wanted to know how old the three were, but since both mathematicians answered Magne:
- If you add up my children's age then the number is 13
- I also noticed that if you multiply the age of my three children, then you will get the number you have in your room in this hotel.
They each went to their own, but Nils was not yet completely satisfied. When they met again, Nils said:
- "I need information to know the age of your three kids," he said.
"Yes, that's right! My oldest child was born in New York," replied Magne.
"Ahh, I know the age of your children," replied Nils.
How could Nils find out the age of the three using the information given?
I do not know
I’ve always enjoyed logic questions; I don’t always figure them out.
Along with basic math skills, thinking like Sherlock Holms, by using logical, deductive reasoning will let the magnifying glass zero in on the correct solution.
The first column is a list of three integers that sum to 13. The second column is the product of these integers, listed in ascending order.
9 3 1 27
8 4 1 32
7 5 1 35
9 2 2 36
6 6 1 36
8 3 2 48
7 4 2 56
6 5 2 60
7 3 3 63
6 4 3 72
5 5 3 75
5 4 4 80
At this point, the reader knows one set of the three integers are the ages of the children. The reader does not know Nils’ room number, but Nils knows it, and still did not know the ages of the children. The reason he doesn’t know is that two of the products are 36, which is Nils’ room number. It’s one or the other but which one? Is it a set of twins with an older sibling, or a set of twins with a younger sibling?
The final statement gives this clue: “My oldest child was born in New York.”
Where the child was born is irrelevant, but from this it easy to see that a single child is the oldest.
The only solution for the children’s ages is 9, 2, 2.