Sixteen Puzzles
On Sundays, Browser readers receive a special edition with puzzles, poems, books, charts, music and more – here's a little taste of this week's edition.
Puzzle Of The Week
The average of 16 different positive integers is 16. What is the greatest possible value that any of these integers could have?
— from The Ultimate Mathematical Challenge by The UK Mathematics Trust
Solution below, after the interview
Interview Of The Week
A.J. Jacobs Talks Puzzles With Uri Bram
LARPer and author A.J. Jacobs talks about his latest book, The Puzzler, to The Browser's Uri Bram; with digressions touching on Oedipus, dogs, mazes, noodles, W.B. Yeats, CBT, ketchup, determinism, and the meaning of life.
On the riddle of the Sphinx:
When Oedipus answered the riddle correctly, the Sphinx was so distraught that she threw herself over a cliff. Which seems like one of the great over-reactions in puzzle history; she needed some cognitive behavioural therapy.
On staying calm:
I’ll never feel comfortable with my impending demise, but I have to accept that feeling. I’m not happy with the way the laws of the universe were set up, but I can’t control them. One strategy I find helpful is to contemplate what the world looks like long after I’m gone. That takes the pressure off: it’s not all about me.
On why people love puzzles:
I don’t think you need a randomised control trial to show that curiosity is one of the great emotions: it’s how we got the wheel, fire, and the mRNA vaccine, etc. (You could argue that Gain of Function research is the bad side of curiosity). Puzzles encourage that, no matter how specific they are.
Puzzle Solution
Puzzle: The average of 16 different positive integers is 16. What is the greatest possible value that any of these integers could have?
Solution: 136. In order to make one number as large as possible, the other fifteen numbers should be as small as possible. Letting x be the largest number, we have:
(1 + 2 + 3 + ··· + 15 + x) ÷ 16 = 16
so (120 + x) ÷ 16 = 16
so 120 + x = 256
and hence x = 136
— from The Ultimate Mathematical Challenge, by The UK Mathematics Trust
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