“We can only see a short distance ahead, but we can see plenty there that needs to be done.”

Alan Turing (23 June 1912 – 7 June 1954)

May 1st 2021 — To celebrate Alan Turing featuring on the new £50 banknote, GCHQ has created their hardest puzzle ever in his honour. So far, we have worked out the solutions of the first four puzzles. Let us take a look at the 5th puzzle of this magnificent challenge! Follow us on Twitter: @INTEL_TODAY

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Puzzle #5 — Foil

Alan Turing provided the theoretical underpinnings for the modern computer. The image of the microchip on the foil is a recognition of that achievement.

Complete the two sunflowers with four letter words spelt outwards from the central 50s, so that adjacent words differ by exactly one letter.

The example on the left shows how BANK can be changed to NOTE in four steps.

Once you have completed the sunflowers, find the central four letter word which differs by exactly one letter from each of the two words it’s connected to through the microchips, to solve the puzzle!

This puzzle is not particularly difficult and all crossword-puzzle aficionados will easily solve it.

Therefore, I would rather take this opportunity to tell you something that is quite remarkable and completely counter-intuitive.

First, you do not have to solve the top flower to find the answer of that part.

Second, you do not even need to find the answer of the bottom flower to solve this puzzle.

I can hear you thinking: “This cannot possibly be true!”

Surely, you must think that I am kidding?

The answer to the top flower

As I have explained last week, the answer of top flower is BLUB.

RELATED POST: GCHQ — Play the TURING Challenge! [How to get the Answer to Puzzle #5… Without solving Puzzle #5]

Now that I have proved my first statement, let us move on to the second one.

The answer to the Puzzle

First, let us take a look at the four lines before the answer of the bottom flower.

Line 4 T * * T
Line 3 B * * *
Line 2 * O O *
Line 1 * L * *
Answer * * * *

Knowing that only ONE character can be changed at any step, we conclude that:

Line 4 T * * T
Line 3 B = = T
Line 2 * O O *
Line 1 = L O =
Answer * * * *

What do we know?

We know little about these lines. Still we know that, going from line 3 to line 2, either the B or the T must survive and of course possibly both.

Now, let us take a look at the big picture!

We already know that the solution of the Top Flower (TF) is B L U B.

So, here is the information we have:

TF: B L U B
P5: * * * *
BF: * * * *
BF1: * L O *

Obviously, the L must survive AND the first letter of BF1 MUST be a B because we can only change two letters to get to TF!

[If the first letter was not a B, then the 4th must be a T. But then, we would have to substitute 3 letters to get to TF and that is against the rule of the game!]

TF : B L U B
PZ : B L * *
BF : B L * *
BF1: B L O *

Please, take a moment to enjoy the progress we have made!

The solution to this puzzle can only be BL*B or BLU* !!!

Back to the Bottom Flower

We know that the first letter is B.

Line 5 T * U *
Line 4 T * * T
Line 3 B = = T
Line 2 B O O *
Line 1 B L O =
Answer B L * *

On line 5, it is obvious that the second letter cannot be O. Indeed, from line 10 to line 5, the first and 3rd letter keep changing, meaning that the 2nd (and 4th) are unchanged.

L10: P * N *
L9 : W * N *
L8 : W * I *
L7 : W * R *
L6 : T * R *
L5 : T * U *

But, there is no word starting with WOI* ! (line 8)

And this means that both letters in position 2 and 3 changed from line 5 to line 2. Thus the last letter of line 2 and 1 is a T.

Line 4 T * * T
Line 3 B = = T
Line 2 B O O T
Line 1 B L O T
Answer B L * *

Back to the big picture!

TF : B L U B
PZ : B L * *
BF : B L * *
BF1: B L O T

As you move from the answer to the Top Flower (TF) to the answer of Puzzle #5 (PZ), you can either keep the U or the B. And keeping the U does not work as BLUT does not exist.

So the answer of puzzle #5 is BLOB.

Notice that we do not know the answer to the bottom flower. And by this method, we have no way of knowing as it could me many words: BLOC, BLOG, or BLOW.

Who cares? We solved the puzzle!

“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”

Arthur Conan Doyle

REFERENCES

Alan Turing — a short biography by Andrew Hodges

The Turing Challenge — GCHQ

GCHQ releases ‘most difficult puzzle ever’ in honour of Alan Turing — The Guardian

The list of all words in the Bottom Flower are:

RENT
RANT
RANG
PANG
PANT
WANT
WAIT
WART
TART
TAUT
TOUT
BOUT
BOOT
BLOT
BLOW
FLOW
FLAW
FLAT
FEAT
SEAT
SENT
RENT

=

GCHQ — Play the TURING Challenge! — How to get the Answer to Puzzle #5… Without solving Puzzle #5 [Think like Turing!]