By Louise Mayor
(Warning: spoilers below for those who haven’t yet tried the Physics World at 25 puzzles.)
October 2013 was Physics World’s 25th birthday. It was also the month in which, unusually for me, I compulsively checked the comments being posted on this blog. That’s because we published a series of five physics-themed puzzles as part of the celebrations, which left me both (a) excited to see if people would enjoy them, and (b) nervous that some loose cannon might reveal an answer and spoil the fun! (It didn’t calm my worries that the very first comment made on the very first puzzle – now deleted – was indeed the answer to the puzzle.)
With more than 1000 comments posted in total, the response to the puzzles was staggering. Commenters posted where they’d come in the rankings (“Hallelujah! #121. That was a tough slog.”), encouraged others to persevere (“Ted, I think you’re nearly there. You’re right about the first word”) and recipients of help were very grateful (“Thanks uszkanni! I’ve been going a bit mental on that one.”)
The infographic above-right shows the number of correct answers submitted to the online answer-checking tool for each of the puzzles, as of early December. We were very impressed with those numbers: not everyone at Physics World HQ was so successful.
Some commenters also debated whether there were mistakes in the puzzles or even more than one possible answer. “Please do better next time Louise,” someone warned me.
Unfortunately, as I couldn’t debate this without giving the game away, my lips were sealed! Today, however, we can announce not only the single-word answers to the puzzles, but also how you can arrive at these answers. Thanks again to Colin, Nick and Pete at the UK’s Government Communications Headquarters (GCHQ), who composed all the puzzles as well as the solutions below.
If you haven’t tried the puzzles yet, and would like to have a go before seeing the solutions, here are the links to each:
Puzzle 1 solution
The plain-text reads: SECOND LAW OF PLANETARY: A LINE THAT CONNECTS A PLANET TO THE SUN SWEEPS OUT EQUAL AREAS IN EQUAL TIMES.
The missing word is MOTION, which when encrypted becomes KEPLER.
The cipher alphabet is:
which begins appropriately: “moving by laws”.
Puzzle 2 solution
To solve, begin by considering statements 1 and 2:
If 1 and 2 are both true, then 10 is false, hence 6 is true, hence 4 is false.
If 1 and 2 are both false, then 10 is false, hence 6 is false, hence 4 is false.
In both cases 4 and 10 are both false. This leads to 5 being a contradiction (as if 5 is also false then that makes 5 true, and if 5 is true, then that makes 5 false).
So one of 1 and 2 is true and one is false. Hence 10 is true, hence 5 is false.
Now consider statement 6.
If 6 is true then 1 is false, and the cat is not alive (shame).
However, if 6 is true then 9 is false, hence 3 is true, hence 8 is false.
But if 1 and 8 are both false then this leads to 11 being a contradiction (as if 11 is also false then that makes 11 true, and if 11 is true, then that makes 11 false).
So therefore 6 is false, and hence 1 is true, so the cat is alive after all (hurrah!).
We can now also say that as 6 is false and 10 is true, 9 is true.
Now consider all the statements in turn:
1. We know this is true.
2. We know 10 is true, so 2 is false.
3. We know 6 is false and 9 is true, so 3 is true.
4. We know 2 is false and 6 is false, so 4 is false.
5. We know this is false.
6. We know this is false.
7. Consider this one last.
8. We know 3 is true and 10 is true, so 8 is false.
9. We know this is true.
10. We know this is true.
11. We know 1 is true, so 11 is false.
So we have 1, 3, 9 and 10 true, and 2, 4, 5, 6, 8 and 11 false.
Now consider 7:
If it is true, then there are 5 true statements, which is consistent with 7 being true.
If it is false, then there are 4 true statements, which is consistent with 7 being false.
So 7 can be either true or false. Hence the only statements that are definitely true are 1, 3, 9 and 10.
Note that although the state of the cat is determined, the state of 7 is undetermined.
Puzzle 3 solution
The three lines of plain-text read:
Self-consistent equations including exchange and correlation effects
Self-interaction correction to density-functional approximations for many-electron systems
Ground state of the electron gas by a stochastic method
These are titles of three of the most cited papers to appear in the Physical Review family of journals, and were authored by Walter Kohn and Lu Jeu Sham; John Perdew and Alex Zunger; and David Ceperley and Berni Alder; respectively.
Lines can be drawn on the diagram linking each physicist’s first name to their surname. The lines for the three pairs of co-authors cross at the symbols α, β and γ – alpha, beta and gamma.
The phrase with the pattern 3, 6, 2, 8, 8 is THE ORIGIN OF CHEMICAL ELEMENTS, a paper published by Alpher, Bethe and Gamow, known as the Alpher–Bethe–Gamow paper, or the alpha–beta–gamma paper. Bethe’s name was originally inserted as a joke to create the pun.
The cipher alphabets are based on the keywords PHYSICS, WORLD and TWENTYFIVE.
The phrase “We hope you enjoy the joke” in the puzzle rubric is intended as a hint to aid computer searching – looking for “alpha beta gamma joke” (or “alpha beta gamma paper”) leads to the answer for those who don’t know about it already.
Puzzle 4 solution
The three lines of plain-text read:
KEPLERS FIRST LAW SAYS THAT THE ORBIT OF EVERY PLANET IS AN ELLIPSE WITH THE SUN AS ONE OF THE FOCI
NEWTONS SECOND LAW DESCRIBES HOW THE ACCELERATION OF AN OBJECT RELATES TO ITS MASS AND THE FORCE ACTING ON IT
THE THIRD LAW OF THERMODYNAMICS GIVES THE ENTROPY OF PESTO AS TEMPERATURE APPROACHES ZERO
In the first law, each letter has been replaced, where possible, by the letter corresponding to the number of letters since the previous occurrence of that letter, using a = 1, b = 2 etc. So in the first word, KEPLERS, the second E has been replaced by c, because the previous E was 3 letters earlier. As a further example, the word EVERY has become hVbit. This is because:
- the previous E is 8 letters earlier in “THE“. Hence h.
- there isn’t a V in the previous 26 letters, so it remains unencrypted.
- the previous E is the first E in “EVERY“, which is 2 letters earlier. Hence b.
- the previous R is 9 letters earlier in “ORBIT“. Hence i.
- the previous Y is 20 letters earlier in “SAYS“. Hence t.
In the second law, a similar system is used except that each letter has been replaced, where possible, by the letter corresponding to the number of letters until the next occurrence of that letter.
In the third law, each letter has been replaced, where possible, by the letter corresponding to the sum of the number of letters since the previous occurrence added to the number of letters until the next occurrence of that letter.
So in the third law, PESTO has become nqsnx because:
- the previous P is 4 letters earlier and the next is 10 later. Hence 14 = n.
- the previous E is 10 letters earlier and the next is 7 later. Hence 17 = q.
- the previous S is 15 letters earlier and the next is 4 later. Hence 19 = s.
- the previous T is 10 letters earlier and the next is 4 later. Hence 14 = n.
- the previous O is 6 letters earlier and the next is 18 later. Hence 24 = x.
Puzzle 5 solution
The seven sets of eight associated words, along with their given words, are:
-ologies and their subjects:
Nobel-prize-winning physicists and their citations:
ANDERSON (POSITRON – 1936)
BOTHE (COINCIDENCE – 1954)
CHADWICK (NEUTRON – 1935)
GABOR (HOLOGRAPHY – 1971)
LAWRENCE (CYCLOTRON – 1939)
NEEL (FERRIMAGNETISM – 1970)
RAYLEIGH (ARGON – 1904)
REINES (NEUTRINO – 1995)
Physicists whose names have been given to things:
VAN DER WAALS (FORCE)
The other half of the pair in doubly eponymous physics equations:
Names of famous physicists (the associated words can be the full names or just the missing parts):
Moons of planetary bodies:
Quantities and the names of their SI units:
When ordered alphabetically, FLOW (RHEOLOGY) fits between NEUTRINO (REINES) and FORD (RUTHERFORD).
Answer: REINESRHEOLOGYRUTHERFORD (REINESRHEOLOGYRUTHER is also acceptable)
Bonus puzzle: Odd ON out
In December 2013 we published a bonus puzzle in our print magazine. For anyone who doesn’t have that handy, the puzzle goes as follows:
A number of particles have collided, but which is the odd ON out?
Bonus puzzle solution
The names can be divided into sections:
The starts and ends can be uncollided and reordered to give:
The remaining letters – the odd ON out – is then T-E-V-A-T-R-ON. The Tevatron was the highest-energy particle accelerator in the world prior to the Large Hadron Collider.