Solutions to Chork's Puzzles

Solutions to the puzzles on the Chork's Puzzle site!

Tuesday, October 31, 2006

Puzzle 42 Solution

The total number of sweets up to bag x is given by x(x+1)(x+2)/6. Using this formula, we equate:
x(x+1)(x+2)/6 < 42 million. ie x(x+1)(x+2) < 252 million. Without solving the cubic equation, we can estimate the value of x+1 by taking the cube root of 252 million, which gives us 631.6

Since x+1 < 631.6, the largest integer x value satisfying the above equation is 630. Hence Chork can pack 630 bags of gems in all.

Answer: 630

Monday, October 30, 2006

Puzzle 41 Solution

Note that the numbers 1-0 on the keyboard form diagonal "columns" on the keyboard, each with 3 letters/symbols below them.

To solve the code, look up the number which the symbol lies above on the keyboard. For instance, ! lies above 1, @ above 2, # above 3 etc and move down that many positions along the "diagonal column" to reach the designated letter. So !1 will be Q, !2 will be A and !3 will be Z

Solving the code, we get: "What is the atomic number of the noble gas which is in the same period as chlorine?"

The noble gas is argon with 18.

Answer: 18

Wednesday, October 25, 2006

Puzzle 40 Solution

The last person will make a count of the total number of black and white hats. If there is an even number of black hats, he will say "black". If there is an odd number of black hats, he will say "white". Thus, the next person in line will work out the number of black hats in front of him and determine whether his hat is black or white. Similarly, everyone else in line can work out whether his hat is black or white based on the previous answers.

Here is an example. Lets say the last person counts 80 black hats and 19 white hats. He says "black" which means there are an even number of hats. The next person in row will count the number of black hats.

Let's say he has a black hat. Then he will count 79 black hats before him. But the number of black hats (including his own) is supposed to be even, so he deduces he has a black hat.

If he has a white hat, he will count 8o black hats before him. Thus, he must not have a black hat or else the last person would have counted an odd number of black hats. He deduces he has a white hat.

Hence, all the remaining 99 wise men can work out their hat colour in this fashion.

Answer: 99

Puzzle 39 Solution

Note that it was a trip to USA. The US $100 note is a portrait of Benjamin (Franklin), the US $10 note is a portrait of Alexander (Hamilton) and the US $2 note is a portrait of Thomas (Jefferson). So Chork in fact had US $112 with him which was just enough for him to get 4 spy kits. Thus one kit costs $28.

Answer: $28

Friday, October 20, 2006

Puzzle 38 Solution

Name the shapes and take note of the first letters of the shapes.

Isoceles triangle


Equilateral triangle

There you go, a Halloween customized puzzle. (:

Answer: Trick or Treat

Puzzle 37 Solution

Take note of the first letters of the italicised words and you will get the first goddess, Artemis.

Next, note that the statements are either Physics or Chemistry statements. classify them according to physics and chem. (Bolded statements are physics statements)

Electric potential of a point is the work done by external force in moving a unit positive charge from infinity to that point.
Reduction of a primary amide using LiAlH4 in dry ether gives a primary amine.

Condensation polymerisation is the combination of monomers with the elimination of small molecules.

For an object undergoing uniform circular motion, speed of the body is constant but velocity is not.
Diffraction is the bending of waves through an aperture or around an obstacle
When charging a capacitor, the energy does not increase instantaneously.
Eddy currents are induced currents circulating in solid conductors when there is a change in flux linkage.

Metals emit electrons when electromagnetic waves of sufficiently high frequency are incident on their surfaces.

Chlorine is a stronger oxidising agent than iodine.
Inertia is the property of a body that resists change in its state of rest or motion.

Simple harmonic motion is the motion of a body whose acceleration is directly proportional to its distance from a fixed point, and is always directed towards that point.
Le Chatelier's Principle states that when a system in equilbrium is disturbed, the equilibrium will shift to annul the effect of the change.

Now, the hint is that chemistry is associated with long and draggy (ie a dash) and physics is associated with short and to the point (ie a dot). By replacing physics statements with a dot and chemistry statements with a dash, we get

.- / - / .... / . / -. / .-

Decoding in morse code, we get the next goddess, Athena.

Answer: Artemis, Athena

Puzzle 36 Solution

Taking note of the first letters of the statements, we have: "Goddess of Desire and Beauty" which gives us the name of the first goddess, aphrodite.

Now, we note that some of the statements are errorneous. Bolded statements are correct.

Girls are generally born with more fat cells than boys.
Ornithology is the study of marine animals. (It is the study of birds)
Decibels is the unit of measurement for the frequency of sound. (The unit is hertz)
Dynamos were invented by Ernest Rutherford. (It is invented by Michael Faraday)

Epsilon, the 5th letter of the Greek alphabet, is used as the symbol of the permittivity of a medium.
Stratosphere is higher up in the Earth's atmosphere than mesosphere. (Stratosphere is lower)
Strontium is more chemically reactive than calcium.

Ohm is the unit of measurement for reactance.
Filaments in light bulbs are usually made of nickel. (The material is tungsten)
Deimos is a moon orbiting the planet Uranus. (Deimos orbits Mars)
Electroscopes are used to measure static charge.
Solder is an alloy of copper and zinc. (It is an alloy of lead and tin)

Infra-red has a higher frequency than microwaves.
Radius is a bone in the forearm.
Ethology is the study of insects. (It is the study of animal behaviour)
Argon is the most common noble gas found in the air we breathe in.

Nb is the chemical symbol for niobium.
Dimenhydrinate is the scientific name for a drug used to prevent hair loss. (It is used to prevent nausea and motion sickness)
Bacillus are straight and rod-shaped.

Etymology is the study of word origins.
Ailurophobia is the fear of dogs. (It is the fear of cats)
Ungulates are animals with toes. (They are animals with hooves)
The explosion that is said to have begun the universe is the Big Bang.
Yttrium has atomic number 39.

Now, according "1" to correct statements and "0" to incorrect statements, we have:

Converting the binary numbers to base 10, and then transforming it to alphabets, we get Hermes.

Answer: Aphrodite, Hermes

Puzzle 35 Solution

Type the message on handphone with dictionary function turned on. You will get the question: "If the difference between two numbers is two and the sum of their squares equals a hundred and thirty, what is the product of the two numbers?"

Now, a - b = 2
a^2 - 2ab + b^2 = 4

a^2 + b^2 = 130

Hence, 2ab = 126
ab = 63

Answer: 63

Wednesday, October 18, 2006

Puzzle 34 Solution

We note that the cube and 4th power must in all contain 10 digits.

Hence, it must be between 18 and 21 inclusive. By trying these few possibilities, we get our answer (18).

On a side note, Gareth does sound alot like myself. Besides we are both 18. (:

Answer: 18

Puzzle 33 Solution

Route taken is as shown, forming SHY, RHYTHM, STY, HYMN, MYRRH, TRY

Answer: 6

Puzzle 32 Solution

Answer: 38

Tuesday, October 17, 2006

Puzzle 31 Solution

The areas below are labelled as such:

Solving, D = 0.55026401E and
B = 1.013852023E

Given B = 2006,
E = 1978.592491
D = 1088.748238

A + B = E + B = 3984.592491 which is the area of the square
Hence, perimeter of the square = 252.4945145
which is the common perimeter

Answer: 252

Wednesday, October 04, 2006

Puzzle 30 Solution

Solving, we have
x = 19.37703728
and y = 23.1589734

So x + y = 43 (nearest integer)

Answer: 43

Puzzle 29 Solution

Identify the fruits in the puzzle and cancel them out. You will be left with the question: "number of loaves in a baker's dozen", and the answer to that is 13.

Answer: 13