Some More Math/Logic Problems To Test Your Wits

I got a surprising amount of emails about this post, with requests for more such puzzles, so here you go (answers after the jump).

1. A deaf-mute man walks alone up to a movie theater counter shortly before a matinee which costs 50 cents to enter. Making no particular gesture (and obviously, saying nothing), he hands the clerk a dollar. Rather than giving him 50 cents in change, the clerk hands him two tickets. The man smiles and nods his thanks. How did the clerk know that he wanted two tickets rather than one?

2. Four people are fleeing the zombie apocalypse in the dark of night, and have to get across a narrow bridge in 17 minutes to survive. The bridge is so rickety that no more than two people can stand on it at any one time or it will collapse. It is also full of holes such that it can only be safely crossed while holding a flashlight. The 4 people have only one flashlight between them. A further challenge is that the 4 people are of different ages and levels of health, such that it takes each a different amount of time to cross the bridge. One takes 10 minutes, one needs 5 minutes, one needs 2 minutes, and one needs 1 minute (all invariably, i.e., no amount of help from a faster person can speed a slower person up). How do the 4 people manage to save their lives by crossing their entire party in the 17 minutes available?

3. A man with a heart condition has to take two medications at the same time every 4 hours or he will die. The medication regime is hard to follow: If he takes none or just one of the needed pills at the appointed time, or he takes that more than 1 of either pill within each 4 hour block, he will have a fatal heart attack. To add to the complexity, the pills of each medication are exactly the same in every respect – color, shape, size, texture, weight, labeling. He copes with this challenge by keeping each medication in its own, clearly labelled pill bottle.

While at his hunting lodge in Northern California, something terrible happens. Just before he is about to take his medications, a earth tremor hits and he falls over. The tremor passes quickly, but unfortunately all but 2 pills have fallen out of one bottle and all but 3 have fallen out of the other. Every other pill is scattered on the floor and he can’t tell them apart! It’s a two day trip back to town where he can help from his pharmacist and doctor, and he has no phone, so he has to figure out how to keep himself alive until he can return to town. How does he do it?

4. 4. A man hands a bank teller a check with the symbols “O – O X +” written on the back. The teller says “Oh, I see you are in the navy!”. Why?

Continue reading “Some More Math/Logic Problems To Test Your Wits”

Two Math/Logic Problems Upon Which To Test Your Brainpower

My family just had the pleasure of a visit from a friend I have known since first grade. Ever since we were kids, my friend and I would try to stump each other with math/logic problems we had heard about (or sometimes, invented ourselves). We went back and forth today, and these two were deemed the most fun — give them a shot if you haven’t heard them before. Answers after the jump.

His best to stump me:

Many numbers are the sum of consecutive digits, for example 29 is equal to 14+15 and 66 is equal to 21 + 22 + 23. Between 100 and 200, there is only one number that is NOT the sum of consecutive digits. What is it?

My best to stump him:

You are in the basement of a house and on the wall are three identical-looking light switches. Two of them are broken and one of them works, but the light that the working switch turns on is in the attic. If you could only make one trip to the attic, how would you determine which of the three switches is the one that works?

Continue reading “Two Math/Logic Problems Upon Which To Test Your Brainpower”

How to walk: the RBC guide

Two easy tips for better walking.

We all learnt to walk very young, normally in the second year of life. It’s completely automatic. Severely neglected babies in orphanages ( update – assuming they are physically normal, see comments /update) get up on their feet and walk (Bowlby, 1952, page 20) just as soon as the adored princelings of modern parents, who cheer on every step with praise and console with hugs after every fall. As with any self-taught skill, our methods are approximate, and we stick with what works.

Skills acquired like this can often be improved. Here is a tip sheet from British sports scientist and walking guru, Joanna Hall.

Ms Hall has a system to sell. If you can’t be bothered to wade through it all, here is the RBC tl;dr condensed version in two bullet points. Continue reading “How to walk: the RBC guide”

History’s Sloppy Summations

UK Labour grandee Denis Healey was once asked to name the best speech he had heard in his four decades in Parliament. He cited a 1959 oration defending the humanity of the Mau Mau prisoners who were murdered by British soldiers in the Hola Massacre. Who gave this passionate anti-Imperialist speech condemning abuse of the people living under British colonial rule in Kenya? (Take a guess, answer after the jump)

Continue reading “History’s Sloppy Summations”

Budget hot tip: the President Trump dollar coin

Scrap $1 bills for a new Trump $1 coin.

The GOP wants to cut taxes, mainly for rich people and corporations, by at least $1.5 trillion over 10 years. They are quite naturally running into trouble finding compensatory cuts. “Dynamic scoring” fiddles can only go so far. Here is a modest contribution. The savings are only $5.5 billion over 30 years, but they are a sure thing according to the GAO in 2011 , and do not inconvenience anybody with a platinum card. It is quite simple:

Replace $1 bills with coins.

Argument and design suggestions below the jump.

Continue reading “Budget hot tip: the President Trump dollar coin”

Rebel Plinths

A proposal for Confederate statues: bring them down to street level.

You wouldn’t get a blog post about plinths anywhere else, would you?

Hear me out. Memorial statuary normally consists of (a) a statue and (b) a plinth. The plinth raises the statue above street level, making it more visible. It also triggers instinctive associations of height with power, dignity and respect. It works even better if you throw in a horse, as with Lee at Charlottesville and Peter the Great in St. Petersburg.

The problem with the Confederate memorials is that they make a racist statement that the Confederate rebellion should not just be remembered, but remembered with respect and admiration. The statement depends as much on the plinth as the statue itself.

So here is a suggestion for dealing with the statues of Confederate soldiers, mass-produced in Northern foundries, that dot hundreds of public spaces in the old Confederacy:

Bring them down to street level.

In the street, they become bronze fellow-citizens, and the gullibility and racism of the men they represent can become as much a part of the civic conversation as their bravery and sacrifice. If they are unpopular, they will be defaced. If they become objects of ridicule, they will sprout frat ties, silly hats and dildos. Them’s the breaks. Let’s see how it works out.

That leaves an empty plinth or two. Don’t spend a fortune taking them away. There’s an empty one in Trafalgar Square in London: it is used for temporary exhibition. Or you can hold a competition for a statue of something or somebody that everybody wants to honour. The Northern foundries will retool to supply as many versions of Martin Luther King as the South commissions.

Footnote for art wonks

There is one striking exception to the plinth norm. When Auguste Rodin cast the famous group of the Burghers of Calais, he lost a battle with the city fathers to install them at ground level. What Rodin wanted was to replace the usual historical distancing from a tragic and violent event with immediacy, shock and empathy. He was rightly confident that the quality of his work would still make the sculpture effective. There is little risk that the mediocre Confederate statuary will compensate in the same way for being brought down to earth. The Burghers have now been brought back down, and stand on a compromise mini-plinth.


The Moment You Realized That You Had Changed

I respect that one reason humanity has rituals that effectively tell people something they already know (e.g., you graduated high school!, you got married!, you retired!) is that even major life changes that were entered into consciously and with great effort do not necessarily work their way into our self-conception unless they are prominently reflected to us by others.

A friend who was a new mother told me a story of her first play group with her son, who toddled tentatively, took a tumble and then cried out “Mommy!”. She instinctively looked anxiously around wondering where on earth the child’s parent was. The women next to her said “He’s yours isn’t he?” snapping her into awareness of how her life had changed forever.

Another example I have seen repeatedly is a long-time renter who finally buys a house. The first time the boiler bursts or the sink pipe breaks, the owner reaches for the telephone feeling sorry for the miserable landlord who has to fix the problem and then realizes that they themselves are the poor sod in question.

The experience of this sort I remember most vividly happened at Stanford Hospital. As a new arrival, I went to the appropriate sub-basement office to get my photo ID. After they handed it to me, I turned the wrong way leaving the office and entered the maze that is our medical center. I finally found a staircase but it wasn’t the one I had come down and I went up too many floors to boot.

I was immediately anxious thinking “I’m lost in a hospital, I’m going to get in trouble.” I walked further and realized I was in a cancer ward…Oh Geez this is really serious now, I’m really in big trouble. I started walking faster, thinking it wasn’t visiting hours and I had no business being around these grievously sick people and I just needed to escape before someone called security and had me thrown out.

I entered a long hallway and saw exit doors, but there was a nurse’s station on the way. As I got closer I saw it was occupied! But she’s looking at her notes so maybe I can slip by, but then, oh no, she’s looking up now and looking right at me, staring at me intently in fact. I am thinking desperately what to say “I got lost! It was a mistake! I meant no harm! Please just let me go and it will never happen again!”

And then she shocked me by smiling and saying “Good morning doctor”.

I literally started to turn around to see who she was addressing and then realized she had been staring at my name tag. I mumbled a response and walked out, trying to suppress laughter at my own expense.

Ever had a moment like that? What was it?

Balkin’s Three (revised) Laws of Robotics

Balkin updates Asimov.

The eminent Yale scholar of, and blogger on, constitutional law Jack Balkin has published a very nice article updating Issac Asimov’s famous Three Laws of Robotics.


It’s a rich short essay, not a treatise; an opening shot in a new debate, not the last word. Read it and comment please.

A few takes of mine. Continue reading “Balkin’s Three (revised) Laws of Robotics”

The Economic Value of Trust

I was digging through some boxes and found an old calabash pipe and stand. It’s the sort of pipe that people think of Sherlock Holmes smoking even though in the books he didn’t (William Gillette added the calabash for a stage adaptation over a century ago and it stuck). pipe

Gourd pipes have gone out of style, being largely replaced by mahogany. That makes this calabash if not an antique at least a curio I could put in my office as a conversation piece. But the decades-old cork ring is eroded and the whole thing is smoke scarred and tobacco encrusted. What to do?

I talked to a local tobacconist who gave me the phone number of a pipe maven in Tennessee who might be able to help. I talked to said Tennessean on the telephone and he said he could probably restore the pipe, so I have mailed it to him.

What is striking about this relative to other business transactions is that this is all done on trust. I don’t know the pipe expert from Adam (not even his last name); he could keep my pipe and there would be nothing I could do about it. On his end, I didn’t send any money so he could do the work and not get paid. But I just had a feeling that I could trust him and I guess he felt the same as we didn’t even agree on the price — we will work that out later on the basis of reason and good faith, jointly applied.

No receipts, no travel to meet in person, no insurance, no contract — all of those costly things are not needed because we exist in an atmosphere of trust.

It reminded me that one of the early stamp collecting companies used to mail sets of valuable old stamps to collectors who were asked to take what they wanted, mail in a check to pay for it, and then mail the stamps directly to the next collector on a list. Anyone could have easily stolen stamps under this system, but apparently few people did because the company was highly profitable.

We spend so much money because of distrust, whether it’s locks on our doors, liability insurance, receipts in triplicate or certified mail. We accept that we can’t trust each other and endure much deadweight financial loss on that basis. We would reap enormous economic benefits if we were more trusting and trustworthy. We think of these things as virtues and they are, but they also have large economic consequences (Did you know that the Amish are so dutiful about paying back loans that banks give them extremely low interest rates?).

I could never prove it, but I think the decline in trust in the country reduces GDP as much as many other factors that are blamed for poor economic performance. Just one more reason why the coming years are not likely to be good ones for our country.

A merry Christmas 2016, or perhaps not

Thoreau was not the only Yankee to be shocked by the naked imperialism of the Mexican War. The Unitarian pastor and abolitionist Edmund Sears wrote the great hymn It came upon the midnight clear in December 1849. I won’t say it’s my favourite carol – Mary MacDonald gets my vote for her gem-like Celtic lullaby – because, being an inhibited Brit, I am embarrassed to shed tears in public.

Yet with the woes of sin and strife
The world hath suffered long;
Beneath the angel-strain have rolled
Two thousand years of wrong;
And man, at war with man, hears not
The love song which they bring:
O hush the noise, ye men of strife,
And hear the angels sing.

As a Unitarian, Sears was unconvinced by the paradoxical orthodox view that the redemption has strangely already happened, in the birth, life and legacy of Jesus of Nazareth, and in spite of his failure, martyrdom, and systematic betrayals by his followers up to our own time. Sears places his hope, as much as any Orthodox rabbi, in a remote eschatological future:

For now the days are hastening on,
By prophet bards foretold,
When with the ever-circling years
Comes round the age of gold;
When peace shall over all the earth
Its ancient splendors fling,
And the whole world give back the song
Which now the angels sing.

But what if we are looking for a more immediate hope today? Savagery continues in Iraq and Syria, the Arctic melts, and another Herod moves into the White House to prepare a larger rerun of the massacre of the innocents, to the complacent plaudits of conservative Pharisees?

I give you an unlikely gold-bearing Mage in the form of investment bankers Lazards. They have been surveying levelized US electricity generating costs for years, and have just published the 10th version. It’s a fat report, but this is the key chart. (Sorry for the poor resolution, go to the report link for a better image.)


The major takeaway is that in the USA the cheapest new coal generation is no cheaper than the most expensive wind and utility solar. (Footnote 1) Continue reading “A merry Christmas 2016, or perhaps not”