On
Difficulty
Part 1: Measurement
“All things are
difficult before they are easy.”
Thomas Fuller 1608 – 1661
Here is a hunt clue :
Three temperature units
At first glance, one would think of the temperature units
like Centigrade and Fahrenheit and if one is stuck there, google to find the
third common unit which is Kelvin.
Their initials would be C F and K.
If you were in a motor hunt, you would probably be on the
lookout for KFC or FCK – both famous ( or infamous ) brands.
There might be other combinations – less famous but still
feasible.
Only when you spot the actual sign in the sector would the
possibilities be reduced – an eerie resemblance to the world of quantum
mechanics where the electron exists as wave and particle until observed and
then it’s one or the other!
However, if you were absolutely new to the world of hunting,
the possibilities from the clue would be far greater. You might actually be
thinking of looking for “Centigrade” and “Fahrenheit” and “Kelvin”.
Who knows? There might be a science shop on the way. That
possibility cannot be ignored.
Or if you have hunted constantly, you cannot disregard a
possibility like TRIOTONES.
In fact, if you were literal in the interpretation of the
clue, and were referring to a thesaurus for synonyms of the words, the
combination would be phenomenal!
So much to look out for – and not a ‘keyword’ in the clue!
Difficulty – can we measure it?
At the outset of the search, where would you place the clue
on the scale of difficulty?
What seems “simple” to some will look “difficult” to others.
Is there a way we can measure difficulty in an unambiguous
way?
What is the purpose of measuring difficulty?
Is it useful for a hunter to assign levels of difficulty to
improve overall hunting skills?
These are a few questions this series of articles hopes to
address.
Before we get into the nitty-gritty of these weighty aspects
of difficulty let’s go back to the hunter who is faced with the clue mentioned
above.
Since the clue is in the context of an actual hunt, there
are certain overall aims that have to be achieved.
Finish the hunt in time; Do not spend excessive or too
little time on each question; Solve as many questions as possible.
Hence, when faced with any particular clue, the hunter must
assign a certain time and effort in solving it.
This is where assigning difficulty levels can be helpful.
How many times have we been caught and led on by clues which finally did not
crack?
When we look back – did we actually assign a “solvability
density” to it ?
Is such an approach feasible?
Difficulty 101 – Just a number
Let’s see if we can at least reach a few practical
conclusions. Looking again at the example given at the beginning of the
article, we can see the issues.
First, although there might be endless possibilities of what
the answer could be, there is a practical limitation on the number of signs in
any sector. This in itself gives us hope that there should be a way to quantify
the difficulty.
If the number of possibilities is X and the number of signs
is Y, we have a model to work on to see if we can estimate a difficulty
quotient.
When Y << X , then chances of coming to a solution is
better than when Y >> X.
Or is it?
I’m sure actual anecdotes can be quoted to prove either
conjecture.
Let’s put actual numbers and see if that helps us towards a
better understanding.
When X= 20 and Y = 8, then the practical approach is to look
at the 8 signs and eliminate the signs that are nowhere near the possibilities.
When X= 100 and Y = 40, then it is not practical to do the
elimination.
In this case, X has to be brought down to a manageable
level.
What is a manageable level?
Is it below 10? If the time for each question is an average
of 8 minutes with a spread of 1 to 30 minutes on them, then even 10 is a large
number to manage efficiently.
When X= 3 and Y = 100, the chances are actually quite good
in getting the answer.
When X= 3 and Y = 6, the chances are better in getting the
answer faster.
Why is this so? It’s not because 3/6 >> 3/100. It is
because Y is smaller.
When X = 1 and Y = 6, the chances are very good in getting
the answer fast.
When X = 1 and Y = 1000, the chances drop just based on the
actual fraction of possibilitythe answer is still obtainable but it might take
longer.
1/6 >> 1/1000
Without even considering the inherent properties of the
questions, we can see that both numerator and denominator must decrease
drastically for improving chances of getting the answer.
If the denominator, Y cannot be decreased due to sheer
number of signs, then X must be minimized.
If both cannot be decreased, then we have an indicator of
difficulty that is insurmountable and a very powerful hint that we must control
the time allotted for this clue.
The above illustration is an important lesson for teams to
consider when they cannot bring X down to a manageable level.
When X has no value OR is a fraction
The nature and variety of clues is such that in the worst
cases we can’t come up with a reasonable value of X. That is when X = 0. When
this happens, we are left with a terrible choice. Let’s compute with actual
numbers.
X = 0, Y = 5 Here,
we can still look at the 5 and reverse engineer to narrow down the possible
answer.
The probability of getting the answer is not 0/5 but 1/5!
X= 0, Y = 100 Here, the time allotted is critical. By
instinct, most teams will allocate some time for whittling down the
possibilities and rounding up the likely suspects for questioning at a later
stage.
To have X= 0 is a rare occasion and the team needs to really
come together to make a decision.
In the vast majority of difficult clues, X lies between 0
and 1. It is in fact a fraction – simply because the entire clue that is not
decipherable is amenable to at least a partial solution.
If X = 1/3 and Y = 5, the “solvability density” is not 1/15
but really 1/5!
This is because if any of the partial solution aligns with
any of the 5 possible answers then that is sufficient to crack the clue.
In summary, if X is brought to any value between 0 and 1
(based on partial cracking of the entire clue), then X can be assigned the
value of 1.
If X = 1 and Y = 100, we have limited time to allocate for
this clue.
First Conclusion
It is paramount that X be reduced to as low a number as
possible. (ideally – 1 )
Defining X/Y as the “solvability density”, we have a
rudimentary mechanism to ascertain difficulty in one of its many dimensions!
This dimension is a pure number – simply based on
possibilities of the solution and the actual number of signs in the relevant
sector.
We will be exploring the other dimensions of difficulty in
later articles. A hint of where the second dimension lies is outlined below.
Let’s come back to the clue – Three temperature units – to
probe a bit more on how X can be reduced.
If we simply disregard the synonyms of the three words, we
eliminate a monstrous number of possibilities.
If we further eliminated short forms of the words – then we
will be simply looking at the following possibilities: KFC, FCK, CKF, CFK, FKC,
KCF.
Now X is 6.
The first 2 are famous and known. Hence, X becomes 2. The
second is not so famous in Malaysia and hence we have X = 1.
The first dimension of difficulty is a pure number X/Y.
The second dimension of difficulty involves the culling of X
from a theoretical maximum to as low a number as possible.
We will go into the details in the Part 2 of “On
Difficulty”.
On
Difficulty
Part 2: Practical
Examples
Real difficulties can
be overcome; it is only the imaginary ones that are unconquerable.”
Theodore N. Vail
Here are 2 questions for a particular sector that you might
be hunting in.
Q1. One cool gas
Q2. Certainly not television!
For Q1, the following possibilities can be considered before
you cruise the sector :
One = I cool =
ice, etc gas = CO, O, H , etc
For Q2, these might be considered :
Television = TV,box
Certainly = surely ,etc
certainly not = no way, etc
The experienced hunter almost immediately starts the search
without fretting over those
considerations which have “etc”.
Why is this so? Because for Q1 ,it is sufficient that one
looks out for any sign beginning with I and for Q2, it is enough to look out
for “box” or “TV”.
There is no need for deep analysis for these 2 questions
since they have revealed some portion of the answer at first glance.
In Part 1, we have defined X as number of possibilities.
For Q1 , X = 1 and for Q2 , X = 1 ( since we are looking for
signs which start with I and signs which have “box” or “”tv” in it )
( Please refer to Part 1 for why X= 1 even though
possibility is partial)
The search for Q1 is made easier since one is only looking
for signs which begin with I ; certainly easier than looking for signs with I
in them.
Y ( which stands for number of signs in sector ) may be
medium (10-40) to large (>50). No matter – since we know what to look out
for!
The example above illustrates how important it is for the
hunter to get X equal to 1. It also illustrates the power of partial
possibilities. There is no need to waste precious time on getting all the
possibilities where “etc” exists.
Finally, the answers are seen.
Explanation : one = I
cool = fan gas = CO television = idiot box
“smart box” is certainly not an “idiot box”
The search ends happily when those two signs are seen.
SECOND LOOK AROUND
It’s another story if both signs are not spotted in the
sector! Difficulties mount up. The thesaurus comes out…
One = ( at least 10
synonyms )
Cool = ( more than 10 synonyms )
Gas = CO, O, H, etc
Taking the top 7 synonyms each for “one” and “cool” and
looking out for CO, O, H at the end of the answer , we would have a few
possibilities ( 7 + 7 + 3 )
X = 17 ( Not too bad
– if top 7 synonyms work out to be correct ; top 7 would be those which you can
expect in a commercial setting )
{top 7 synonyms for one = ace, lone, sole, single, united,
complete, satu }
{top 7 synonyms for cool = ice, chic, cold, chill, smart,
excellent, wonderful }
There being no key words – “One cool gas” would still be crackable at this stage.
For Q2 , Certainly = ( at least 15 synonyms )
“Not television” = Not TV ( not is deletion indicator )
Difficulty reduces as the whole clue looks like a synonym
for “certainly” taking out the letters TV or Box.
The only valid synonym becomes “ Positively”
Taking out TV from Positively, we have POSIIELY
Such a sign looks unlikely , unless it a Double Jeopardy or
POS 2 ELY!
Look out for signs with letters P,Y in them.
X = ( number of signs with P,Y,L in them ) ( probably single digit very good )
Writing down all such signs is important as they can be
referred to later.
In summary: Always look for the simpler solutions before
engaging other possibilities.
Second Conclusion
X for Q1 is high
(17) ; X for Q2 has come down from 15 to single
digit
If Y is in the 100s, then the difficulty goes up.
In both cases , it is worthwhile to list down the signages
that partially satisfy our possibilities.
If time was of the essence and one had to choose which one
to look out for , would it be Q1 or Q2?
Q1 looks difficult for X to be brought down. In Q2, it was
possible since it had a keyword – NOT which restricted the number of synonyms.
Q2 is the better candidate for a solution under time
pressure.
In the case of Q1, it is not easy to search for presence of
multiple synonyms among the signs.The mind can wander and miss out some of
them. It probably requires division of work among the team and several rounds
of scanning.
We get a glimpse of how it is possible to reduce X from its
original high value to a more manageable one.
The presence of a keyword allows limitations to be set on
possibilities. This decreases X and increases “solvability density”.
The second dimension
of difficulty involves the reduction of X from a high initial value to a single
digit-value by the application of the keyword in context.
By this reckoning, Q1 is ‘tougher’ to solve than Q2 since
there are simply more possibilities.
It does not mean that one gives up on Q1. It means that it
is better to solve Q2 first and then work on Q1.
In the example above, Q1 and Q2 occur in the same sector.
However, the principle applies throughout the course of the
hunt.
As one looks at upcoming questions and assigns an X value
for each of them – they will fall into several categories : X = 1 ; X = 0 ; X =
single digit ; X = double digit . The questions with X= 0 & double digits
are the ones where the solvability density must be increased by skilled
application of keyword in context.
In the following
examples , see whether you can assign a value of X to each of them and grade
them in order of difficulty .
Q3. USA Today? I’m shocked!
Q4. Honey voice of gold
Q5. In Great Britain to the west – it’s a star
See whether you can actually predict the answer .
If you can – you have actually reduced X to 1!
In Part 3, we will explore the varieties of difficulty
encountered in clues. This might give us a better handle on how to reduce X
from either 0 or double digit figure to single digit. Some kind of
categorization would be helpful in assessing and actually reducing
possibilities in case of double digit.
Where X= 0 from the start, we need to have a special look.
On Difficulty – Part 3
“Try
again. Fail again. Fail better.”
-
Samuel Beckett
Difficulty & Delight
Gamers
usually come in two categories- casual and real. A game like “Angry Birds” is
just difficult enough to be diverting –
a good fit for casual gamers. Real gamers demand aesthetic difficulty. Such a
game is “English Country Tune”. Many reviews exist on the net. “The sense of
delight from solving what initially looks impossible is immeasurable.”- is a
sentence in one such review.
Why
is that a delight? In fact, everyone has gone through this feeling in many
forms ever since infanthood. As the growing infant learns to walk, talk and do
a whole bunch of things – the pleasure of achievement felt by both infant and
parent is indescribable.
Real
gamers have never lost that feeling of wanting to try something impossible and
then succeeding bit by bit. Casual gamers get put off by excessive difficulty.
After many, many tries – if one cannot see progress – one will switch to less
difficult stuff – which is fine. What determines the choice of the casual and
the real gamer in either case is locked in the mysteries of “difficulty”.
What
kind of “difficulty” encourages one and what kind of “difficulty” discourages
one? How much time can one give in any activity to crawl up impossible cliffs?
What is the nature of the special delight in unlocking the difficult? Why are
some difficulties orgasmic and some ho-hum?
To
answer these questions to some extent, we need to categorize varieties of
difficulty. As it goes in gaming, so it goes in hunting. Both Casual & Real
hunters expect some kind of difficulty in the hunt. And it will useful to both
of them to know the kinds of difficulties that exist so that they discern and
recognize the types in the future.
Types of Difficulty
Type
1 : Insufficient Knowledge
In the old days ( before browsers ) real hunters
had a special box carrying all the important reference material – books on
botany and zoology, single or double volume encyclopaedias , books of lists,
almanacs , atlases , historical and literary references et al. Along with
several dictionaries and Roget’s Thesaurus , a hunter’s arsenal was complete.
The box would occupy centre seat behind
- throughout the hunt! Searching was not easy as one had to somehow narrow the
options of what to look out for. Manual browsing was a skill that one picked up
slowly.
Nowadays,
all knowledge is at our fingertips. Google knows all and sees all. Even
esoteric questions on obscure facts can be broken inside a minute or two.
Sometimes the field is wide and still requires a kind of culling to be
successful.
Nevertheless,
it is assumed that most of the ‘common’ facts will be easily available via your
electronic device. Let’s look at a few types of ‘knowledge’ questions.
Q. Uluru is the original name.
A. Ayers Rock
Quite
a straightforward question. You have to find out its present name. It’s a pure
knowledge question.
Q. Who’s O’Riley in its own reflection? A. AB
If
you just googled “o’ riley” it might take you sometime to narrow down which o’riley
is really being referred to here. However, “who’s o’ riley” will straight away
pinpoint the correct one.
Q. AmBank contracted to India its founder A. Reliance
Here,
googling “AmBank” or “AmBank’s founder”
will lead you on a wild goose chase. However, if you do the cryptic part first
by contracting AmBank to Amban and add I to get Ambani , then it would have
been a cinch to reach the answer.
So,
even knowledge based questions can be tricky and one must be aware of another
approach occasionally.
Try
your hand at cracking this clue :
Q. Shakespeare’s spur
Type
2 : Unfamiliar Technique
The
unfamiliarity in this type of question lies in the need to separate seemless
into seem and less.
Then
we have seem less look à SEE M
(less LOOK ) à SEE M
less SEE = M = MayFirst
Q. It was foretold the day before the last boom panic A. DEMC
The
unfamiliarity here is the usage of “foretold” as homonym indicator , thus
reducing DAY to DE.
Q. Yummy crisp cheese type sold here A. SHARP
Without
separating yummy and crisp and cheese
type it’s pretty hard to crack this clue.
The
first and third questions do not succumb
to partial cracking. An unfamiliar style has to be encountered at least once
before our brains become adept in deconstructing similar questions later.
Unfamiliar styles often lie in territory where cryptic rules are stretched
beyond the limit. It is a kind of no-man’s land where minefields lie hidden.
The rules of decent warfare have been cast aside and in its place we have the
terrorist manual. After a while, we learn to cope with these asymmetric methods. Losing a few phantom limbs in the
process of crossing the minefield, we become armed with ‘illuminati’ knowledge.
Next time, we say to ourselves, we won’t step on certain kinds of topsoil!
A
real hunter will have over the years categorized the individuality of the CoC
with regard to unique techniques. In doing so, the hunter narrows the scope of
search. Once done, the partial cracking
procedure can proceed.
Try
your hand at cracking & explaining
this clue based on an unfamiliar technique.
Q. From bough, leaves drop, though silently at first. A. Buffalo
Type
3 : Artifice
Occasionally,
there are some questions where no leverage can be applied to prise open the
hidden doorway. Only with approximate and calculated guesses can the potential
answer be corralled. Though there are no unfamiliar techniques being used, the
placement of words is such that you feel you are walking a Penrose stairway or
staring at an Escherian woodcut. These are the rarest of birds. Much can be
learned from any one of them. Something akin to adjusting the eyes so that the
image pops up from a stereographic image happens in the mind when you
successfully solve one of them along the route.
Most
of these clues have X as a fraction.( see earlier articles for explanation of X
)
Q. The alternative to the same writer is to return separately and
substitute oddly.
Q. They are both represented within, if taken literally.
Q. Recalling it is no good, man! Goes without saying!
Answers
are from the pictures below:
Summary
Hunters
can now fashion their own strategies on how to breakdown a difficult question
in the context of a hunt. These few rules form the basis of decoding
successfully.
- Reduce X to 1 as far as possible
- Reduce Y to as low a figure as possible
- Use partial cracking of clue ( X
is a fraction ) as basis for 1 & 2
- Categorize the difficulty as 1 of 3 types
- Build your database of unfamiliar
techniques
Jay
Menon
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