The latest puzzle from The Well-Tempered Spreadsheet:Many years ago, a large jetliner crashed into the ocean. No one could ever find the plane or any of its passengers or crew. The outside world did not know that there were many survivors. They made their way to two separate islands.The islands, known as Uniformia and Ignoramia, were uninhabitated before the survivors arrived. They made pleasant lives for themselves. There is always plenty of food and water. The weather is always good. No one ever leaves, there are never any newcomers, and there will never be a rescue. By now, everyone is too old to reproduce. There are never any accidents, murders, or suicides.People on both islands die only from natural causes, but in a very unnatural way. If anyone dies in a particular year, it happens at noon on September 1st. It is even possible to find out exactly when each person will die, but most would rather not know.It is now the afternoon of September 1, 2012. One hundred people remain on Uniformia. They will die at a constant rate over the next ten years: ten in 2013, ten in 2014, and so on through 2022. The average life expectancy of the people on Uniformia is now 5.5 years. Their life expectancy will decline as each year passes.There are also one hundred survivors on the island of Ignoramia. Their easy island life has never demanded abstract thinking, which is good since most Ignoramians hate mathematics. In particular, they believe that algebra is unnecessary.Franz is the only one on the island who likes math. He calculates the average life expectancy of the people on his island. It is only 1.6 years. This is alarming news to the other Ignoramians.Franz offers them a deal. If they put him in charge of the island, he promises that next year the average life expectancy will improve to 2 years. The year after that, it will be 3 years, and then 4, and then 5.The Ignoramians do not understand how this is possible, but they trust Franz and agree to his deal.As the years pass, the average life expectancy changes exactly as Franz promised:Date (September 1) -- Average Life Expectancy (years) 2012 -- 1.6 2013 -- 2.0 2014 -- 3.0 2015 -- 4.0 2016 -- 5.0The Ignoramians are grateful to Franz. What did he do to improve their life expectancy?

Nothing, he just figured out that the distribution was something like:list = Join[ConstantArray[1, 50], ConstantArray[2, 10], ConstantArray[5, 10]]{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}N[Mean

• ]=1.71429N[Mean[Select[list - 1, # > 0 &]]]=2.5N[Mean[Select[list - 2, # > 0 &]]]=3So if the distribution is decreasing, with a large part of the population dying in the first 5 years, but with some (probably Franz) living long enough that their life expectancy in 4 years is 5 years , you'll have the described effect.

That's right, Franz did not have to do anything. He just figured out that the average life expectancy was going to change as he said.For now, I will hold off on revealing the actual Ignoramian amortization schedule, in case anyone wants to work it out on their own. The follow-up question is: what is this puzzle really about?

It's about bond maturation and the duration of the Fed's remaining portfolio.BTW, as long as a population has at least 4 people with a 9 year life expectancy at the start, then an evil program of geronticide can create that profile.

QuoteOriginally posted by: outrunThat's the technical part.However the behavioral part is that Frantz took control over the island by fooling the people, taking advantage of outsmarting, not fully informing them, and effectively doing nothing, havingnegative added economical value for his clients.Frantz will probably sink the island too if that created addition value for him.Frantz has an ethical problem.Maybe! Given that his fellow islanders hated math, Frantz could never have fully informed them. Trying to make the islanders understand (math! yuck!) would have created even more negative added economical value for his clients.It looks like a fair exchange negotiated between consenting adults -- the islanders got what they wanted (knowing that their life expectancy would increase) -- and Frantz got what he wanted -- power.Also, the islanders have as much an ethical problem as Frantz. Why did none of them take any responsibility to verify Frantz's claims, delve into Frantz's policies, or determine what would happen if they didn't put Frantz in charge?

Initial distribution is:70 x 1 year20 x 2 years5 x 3 years2 x 4 years3 x 9 years

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: outrunThat's the technical part.However the behavioral part is that Frantz took control over the island by fooling the people, taking advantage of outsmarting, not fully informing them, and effectively doing nothing, havingnegative added economical value for his clients.Frantz will probably sink the island too if that created addition value for him.Frantz has an ethical problem.Maybe! Given that his fellow islanders hated math, Frantz could never have fully informed them. Trying to make the islanders understand (math! yuck!) would have created even more negative added economical value for his clients.It looks like a fair exchange negotiated between consenting adults -- the islanders got what they wanted (knowing that their life expectancy would increase) -- and Frantz got what he wanted -- power.Also, the islanders have as much an ethical problem as Frantz. Why did none of them take any responsibility to verify Frantz's claims, delve into Frantz's policies, or determine what would happen if they didn't put Frantz in charge?It's in the nature of islanders to not be bothered with that type of stuff, ..as long as thing are fine... The thing they need to do is hire accountants and lawyers to keep Frantz under control! edit: reading it again: there wasn't even a problem untill Frantz started calculating and telling things to people! He created the concept of fear, and misused it to take control of the island. Two more years with Franz the whole economy will revolt around installing body-scanners at every palm tree.But isn't it unethical to withhold the life expectancy numbers? Once Frantz knows, he has to tell people, doesn't he?

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: outrunThat's the technical part.However the behavioral part is that Frantz took control over the island by fooling the people, taking advantage of outsmarting, not fully informing them, and effectively doing nothing, havingnegative added economical value for his clients.Frantz will probably sink the island too if that created addition value for him.Frantz has an ethical problem.Maybe! Given that his fellow islanders hated math, Frantz could never have fully informed them. Trying to make the islanders understand (math! yuck!) would have created even more negative added economical value for his clients.It looks like a fair exchange negotiated between consenting adults -- the islanders got what they wanted (knowing that their life expectancy would increase) -- and Frantz got what he wanted -- power.Also, the islanders have as much an ethical problem as Frantz. Why did none of them take any responsibility to verify Frantz's claims, delve into Frantz's policies, or determine what would happen if they didn't put Frantz in charge?It's in the nature of islanders to not be bothered with that type of stuff, ..as long as thing are fine... The thing they need to do is hire accountants and lawyers to keep Frantz under control! edit: reading it again: there wasn't even a problem untill Frantz started calculating and telling things to people! He created the concept of fear, and misused it to take control of the island. Two more years with Franz the whole economy will revolt around installing body-scanners at every palm tree.But isn't it unethical to withhold the life expectancy numbers? Once Frantz knows, he has to tell people, doesn't he?I would say the opposite. The people can't prove him right or wrong and so they have to believe him. He's ambitioning to be a sect leader. He doesn't need math for all this! He's just going to make them drink a leathal potion every September 1st around the "lord of the 99%" so that Xenu will come and save him.Yipes! That's Mathentology. Frantz proves that demonic demographers demolish democracies.

Yes, it's about bonds. I was thinking about the outstanding marketable U.S. Treasury debt. The Treasury recently announced its success in increasing the average maturity by more than 30% since 2008. But the new debt issuance has been much shorter than the existing debt. How could the average maturity have increased?Since the Treasury maturities are very front-loaded, like the death schedule of the Ignoramians, the average maturity tends to increase on its own. I found that if the Treasury had left the portfolio alone, or had always matched its new issuance to the pattern of outstanding maturities, then the average maturity would have increased twice as fast as it actually did since 2008.The Treasury's issuance practices slow the "natural" increase in average maturity. I gave a presentation on this topic that was well-received. However, some others with whom I've shared this material cling to the conventional view that increases in average maturity must be the direct result of the maturity structure of new issuance.

yegulalp,I wonder how you solved it. Did you use algebra, trail and error, or some other method?I'm sure you also saw that you could replace the 3 in year 9 with one each in 8, 9 and 10.Thanks,Win