Stikkord: gåte

Aaargh, jeg hater slike gåter med løsninger som er totalt uintuitive. Samtidig elsker jeg dem. Jeg har tidligere blogget om Monty Hall-problemet. Her kommer en ny gåte som også handler om sannsynlighetsberegning, noe vi mennesker er usedvanlig dårlig til rent intuitivt. Det er vel også mye av årsaken til at folk tror på mirakler og må forklare «umulige» hendelser med noe paranormalt…

Gåten har to ulike formuleringer:

1) Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?

2) Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

Hva tror du?

Paradokset ble først beskrevet av Martin Gardener i Scientific American i 1959. Men noen tiår senere laget Marilyn Vos Savant, kvinnen som også er kjent fra Monty Hall-problemet, to nye varianter av gåtene. Først i 1991:

A shopkeeper says she has two new baby beagles to show you, but she doesn’t know whether they’re male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who’s giving them a bath. «Is at least one a male?» she asks him. «Yes!» she informs you with a smile. What is the probability that the other one is a male?

Og i 1996:

Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman’s children is a boy and that the man’s oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

To andre varianter formulert i forbindelse med en undersøkelse utført i 2004 er:

Mr. Smith says: ‘I have two children and at least one of them is a boy.’ Given this information, what is the probability that the other child is a boy?

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Diverse Vitenskap

Da jeg var liten fortalte min far oss en gåte som jeg aldri klarte å finne svaret på. Gåten var av en slik art at man kunne bli gal av å tenke på den, fordi den på mange måter var litt magisk. Man fikk alle fakta servert på bordet, og løsningen burde være enkel, men likevel var det noe som ikke stemte. Man starter i den ene enden, og uansett hvor nye man følger tråden i historien, så ender man opp som et spørsmålstegn.

I voksen alder har jeg støtt på samme gåten på nytt, i ulike varianter. Jeg har en variant av gåten rammet inn og plassert på en hylle på toalettet, slik at gjester blir stående og gruble mens de gjør sitt fornødne. (Idéen var min ekskones.)

Lesere av denne bloggen vil sikkert sette pris på gåten, så her kommer enda en variant:

The Thompson triplets were sitting around watching television. The reception was so bad that they decided to throw away their TV and go buy a new one. They checked their wallets and found that they only had $10 each. So they took their $30 to a second hand store.

They met a salesman who told them he had a TV for sale for $30. So they gave him $30 and took the TV.

However, when the salesman went in the back of the store he realized that the price was supposed to be $25. So he ran back outside to give them their $5 back. But when he realized they had each paid $10 he didn’t want to make it confusing so he only gave them $1 back each and he kept the other two dollars for himself.

OK, let’s recap. They paid $10 each which is $30 total. The salesman gave them back $1 each and he kept $2 for himself. So they actually spent $10 each minus $1 each. Which means they spent $9 each. 9 X 3 = $27, The salesman kept $2. That’s a total of $29.

Where’s the other dollar?

Diverse Personlig

Ny gåte fra bloggen til den eminente Richard Wiseman. Denne tok det meg et par minutter å løse. Hvor lang tid bruker du uten å google svaret?

Spørsmål: Hva er spesielt med dette diktet?

I often wondered when I cursed,
Often feared where I would be
Wondered where she’d yield her love
When I yield, so will she.
I would her will be pitied!
Cursed be love! She pitied me.

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