Season's Greetings

Is it to do with the twins being born on 29 February and so having a birthday every four years - although I can't quite get my head round seeing how that would work.

 

No, but thinking about when in the year they might have been born is thinking along the right lines.

 

Getting close ........

 

12 noon, the clock is wrong.

 

I think the answer given is too brief for full comprehension (by me at any rate) and requires clearer explanation.

Perhaps along the line that we are now dealing with two sets of twins (hence your reference to it being before IVF). So comprising a younger set (brother & sister) and an older set (likely two sisters but could be brother & sister) - one of whom would be the speaker. The speaker is thus referring to the younger twin brother. Either this or something else but please do reveal.

 

Spot on and I would have just added - time to buy a new clock.

 

Will now post my Ancient Greek Paradox puzzle and see how you get on with it and you will see why it is classed as a paradox.

"The Law student’s dilemma"


The teacher Protagoras agrees to take the penniless Euthalus as his student on condition that Euthalus pays him for his tuition upon winning his first court case.

Later (after a few years of tuition with Euthalus now practising on his own) and impatient for his money, Protagoras sues Euthalus for it, even though Euthalus has not yet won a case.

Protagoras argues that if he wins the case, he will be owed the money, and if Euthalus wins the case, he is still owed the money on the terms of the original contract.

Euthalus, on the other hand, claims that if Protagoras wins the case, Euthalus still hasn’t won a case, so he cannot be due to pay. If he (Euthalus) wins the case, the terms of the original contract are voided, so he still does not have to pay.

Who is right, Protagoras or Euthalus?

(If you think along the lines of how the court would rule on the situation, plus any subsequent response or action by either party, that might help)

Will provide the most likely outcome after Christmas.

 

Catching up on this posting I see things have passed me by. What I thought was you providing a solution was merely you confirming they were actual twins. Now I see it is likely to be a leap/time of year conundrum and post if anything springs to mind.

 

I will reveal the answer now, then I can look at your latest puzzle.

The answer lies in the twins' births, and the comment made about their ages, spanning midnight on New Year's Eve / New Year's Day.

So let's say the older twin was born around 23.45 on 31 Dec 1900, and the younger one at 00.15 on 1 Jan 1901.

The older twin makes the statement about their ages, beginning a few seconds before midnight on 31 Dec 1919 and finishing just after midnight on 1 Jan 1920.

So "last year" was said in 1919 and so refers to 1918 - the year in which the younger twin turned 17, but was for the first 15 minutes of the year still aged 16.

And "next year" was said in 1920 and so refers to 1921 - the year in which the older twin would turn 21.

 

Thank goodness you did, I would never have got there in a month of Sundays.. I wonder how that saying came about?

 

Confirmation then, I am no good at brain teasers. Could never cope with 'mental arithmetic' either :-(

 

As with all Paradoxes, solutions can vary but the most obvious is as follows:

Protagoras has the best argument even though he knows he will lose the case. The court will have little choice but to rule against him and Euthalus would not have to pay.

However, if Protagoras brings another case against Euthalus he would surely win, because as Euthalus won the original case (because Protagoras lost) the contract condition would be fulfilled, and the court would order that the money be paid.

There is a caveat of course: the above would apply if Euthalus conducted his own defence. Had he appointed another lawyer to represent him, the victory (it could be argued) belonged to the Lawyer and not Euthalus. However Protagoras could challenge that it was a ruse to avoid Contract fulfilment, even if the lawyer was working 'pro bono'. If paid a fee, doubly so as it was proof that Euthalus had sufficient funds to pay Protagoras what he was contractually owed.

Other solutions may present themselves of course

 

Believe it or not I did not check Wiki for any version or solution to the Paradox. My version quoted as an authentic 'Ancient Greek Paradox,' was in a book (a 2016 Christmas present as a matter of fact) which I more or less quoted verbatim (apart from an italicised comment); and likewise the solution. It made no reference to Euthalus not entering the profession of law, so of course I would not know that, and reading Wiki I think it just represents one of several versions of the Paradox.

In truth I just liked the concept of Protagoras bringing a lawsuit in the full knowledge he would lose, thus paving the way for it to count as a win for Euthalus, and allow him to further sue for payment. Even the caveat of Euthalus not conducting his own deference was considered weak, and I see Wiki mentions was probably also not lawful in a Greek court at that time.

Hadn't given it a thought but I wouldn't be at all surprised. However just as you checked Wiki, a quick Google reveals its Etymology comes from Greek protagonistes..."actor who plays the chief or first part" ...from protos ("first") plus agonistes ("actor, competitor"), so guess that wins the day.