One Last Agent

Congratulations, your plan worked and the Fire Nosed Bear attacked one of the agents and all the minions. They had to be airlifted out to the nearest hospital. Unfortunately, one of the agents stayed behind in the camp and was not injured, and he's hopping mad. He doesn't care about the bear skin rug anymore--he just wants to kill the bear for attacking his friends! You must stop him!

You saw him loading up his pack with grenades which tells you he plans to throw live grenades into the bear den! This gives you an idea. You will use your motorcycle cargo net to make a shield in front of the bear den so that when the agent throws a live grenade into the den, it will bounce right back at him. Thank goodness you brought your motorbike! You will use the sedatives you took to sedate the bear and then set up the net. However, the holes in the net are about the same size as the grenade so you're worried it might slip through. Fortunately, you brought a pack of 100 rubber bands with you. How can you tie the rubber bands onto the cargo net to make sure the grenade bounces off instead of passing through?

Adrenalin Darts

Congratulations, you placed your microphone 10 cm above the base and were able to hear the V.A.L.A. agents discuss their plans for the Fire Nosed Bears! It turns out they only have two agents and five mission specialists to help them. But they only need to capture one Fire Nosed Bear. Apparently, some rich donor to V.A.L.A. will donate ten million dollars if he can get a Fire-Nosed-Bear-skin rug. Their plan is to tranquilize the bear and then kill it--they don't risk shooting it because that might ruin the fur. And that gives you an idea!

Your plan is to replace the tranquilizer solution with Adrenalin--a substance that will give it extra energy to attack the V.A.L.A. agents and minions after they've shot it! You sneaked into the camp last night and discovered that they are using 5 cc TeleDart syringes filled with 3 cc of tranquilizer solution. You will have A.A.K.V.O. deliver some identical replacement darts filled with Adrenalin via quad-rotor so you can swap them out tonight. But how much Adrenalin solution should you use? The bear is larger than average and weighs 300 pounds. The dose of Adrenalin is 0.01 mL of stock solution per kilogram. How much of the stock solution should be used for the bear, and how much water should be added to dilute it up to 3 cc?

Hint:  cc = cubic centimeter

Parabolic Microphone

Congratulations, you were able to ride your motor bike to a forested area just outside the V.A.L.A. camp without detection. Now you must spy on them to learn their plans for the Fire Nosed Bear. You brought along your folding parabolic microphone but you lost the instructions for how to assemble it!

A parabolic microphone works by bouncing the sound waves off of the dish toward the microphone in the center. A parabola curve has the unique property that all waves coming straight in get bounced toward the central focal point (point F below) no matter where they hit the dish! But you need to figure out where that central point is--how far above the base must you place the microphone?

Your parabolic microphone is 50 cm wide and about 15 cm deep. The equation that describes the dish from the side is y = x²/40. First graph your parabola on graph paper with (x=0,y=0) at the bottom center of your paper.

The steepness of the curve is called the slope--like a ski slope--where the bigger the number, the steeper the slope. In math, you can get an equation that gives you the slope at every point x if you have the equation of that curve--which you do! This is called the derivative. Taking the derivative of your parabola equation gives you this:  slope = x/20. Now calculate the slope at x={0,5,10,15,20,24} and add those values to your graph.

To figure out where to place the microphone, you only need to figure out where one of the sound waves would bounce off the dish and end up. The easiest point is where the wave comes down from the top (in the diagram above) and bounces off the dish at a 45 degree angle and goes horizontally to the microphone. So you just need to find the point on the curve where the slope is 45 degrees. Unfortunately, the slope from the derivative (equation above) gives the slope as a ratio of the rise over the run, as shown in the diagram to the right. What is the slope that corresponds to a 45 degree angle? Once you find that, you can find the point that is at the same height as the microphone. Then you can finish building your parabolic microphone and listen in on the V.A.L.A. agents!

Hike or Bike

Congratulations, you destroyed all of the V.A.L.A. transmitters with your perfectly placed EMP bomb! Now you're in China on your way to save the Fire Nosed Bears.

You've ridden your motor bike to the top of a nearby mountain coming down the road from the north (you are now at the red X below). Now you must either hike to the V.A.L.A. camp (yellow pin below) which is 32 km in a straight line or stay on your motorbike and take the 53 km path through the valleys shown by the yellow path with red dots below.

You can hike at 4 mph without stopping. Your motorbike can go 10 mph but the radiator is busted so you must stop every 30 minutes and let it cool down for 15 minutes. Should you bike or hike to get to the camp in the shortest time?

EMP Bomb

Congratulations, you've discovered the next V.A.L.A. secret mission! All the mission specialists are leaving today, and you'll leave with them. However, before you go, you want to prevent V.A.L.A. from using the cameras in the future to kill the Bengal Tigers. The cameras send their images to several dozen transmitters also placed in the forest, as shown on the map below. You will use an A.A.K.V.O. Electro-Magnetic Pulse Bomb to destroy the transmitters!

You need to tell the pilot the coordinates to detonate the bomb so it will cover all of the transmitters in the map below. The bomb can destroy all electronic equipment in a 300 square-kilometer area. The distance between the lines on the map is 2.5 km. What are the coordinates for the bomb detonation?

V.A.L.A. Minesweeper 2.0

Congratulations, you uploaded the new code to the V.A.L.A. supercomputer. When the operation started early this morning, all the agents went to the wrong place and they didn't get any tigers! By noon, they realized something was wrong and recalled all the mission specialists. While you are waiting to see what they do next, you noticed that they uploaded V.A.L.A. Minesweeper 2.0! You might as well play it while you are waiting.

Mines left:

V.A.L.A. Reminder: Humans Good. Animals Bad.

Bengal Tigers

Congratulations, you sneaked into the V.A.L.A. Supercomputer room and made a copy of the mission code without being detected. Your partner back at an A.A.K.V.O. base was able to modify the code so it will send the V.A.L.A. minions to the wrong locations. All you need to do is to sneak back into the room and upload the new code. However, they've changed the locks!

After you opened the lock to free the kittens (which was blamed on the P.E.T.A. undercover agent), they decided to upgrade to Super-Tuff^® six-digit locks! Here are the hints on the new lock:

• Reel A and reel F are the same number
• The last reel plus reel E equals 1
• Reel C has the highest digit
• The answer is divisible by 5
• The digits total 16
• The smallest and largest digits have a difference of 7
• Reel C plus reel B is 4 more than reel E plus reel D

The Plan is Revealed

Congratulations, you are now a V.A.L.A. mission specialist! In today's briefing, you learned the plan for Operation Agent Gerbil. You will go out into the woods and place over one thousand cameras in the forests of India and Bangladesh. A V.A.L.A. supercomputer will then track the Bengal Tigers and find their dens. Then on Tuesday, the mission specialists will be sent out to the locations identified by the computer so they can shoot and kill the tigers! Your plan is to modify the code in the supercomputer so it will send the agents to the wrong locations and the tigers will be safe. You found a door marked V.A.L.A. SUPERCOMPUTER but there's lock on the door. You need to open the lock, make a copy of the code so you can figure out a way to change it, and then lock the room again so they don't know you were in there. Here's the text written on the lock:

• Reel A has the lowest digit
• Reel E times reel D is 49 more than reel C times reel B
• Reel B is 8 or 2
• Reel A is a square number > 0
• The answer is above 14583

Good Luck!

Final Test

Congratulations, you decoded the message and found out that there was another spy, Joan Horton from P.E.T.A., also undercover and she got blamed for your kitten rescue! You let her know they were looking for her and she escaped safely.

Your classes have resumed. You learned about their secret prime factor code (which you figured out yesterday) and more ways that humans should use animals. At the end of your training, Herman T. Sherman came in for the final test:

This picture shows why we must eat all the animals of the earth. When human water babies (blue) eat the flesh of animals (pink), we see the light and wisdom of God (yellow). One only needs to look at this picture to understand the mission of V.A.L.A. For your final test, draw a horizontal line with a point on it. Now draw a circle around it. Next, draw another circle starting from the intersection of the first circle and the line. You will become a V.A.L.A. mission specialist if you can figure out exactly how many times taller is the football of God's wisdom than it is wide. And then tomorrow I will tell you about Operation Agent Gerbil!

Wow, that seems easy. You should soon be a V.A.L.A. member with inside information.

Secret Code

Congratulations, you figured out the combination and freed the baby kittens! But now the V.A.L.A. leaders are furious! They have canceled classes for the day, allegedly to give the new recruits a day off. But you know that they are frantically searching the compound for the spy. You are hiding in the woods nearby and your partner has sent you the following message which was sent to the V.A.L.A. tablet that A.A.K.V.O. still has:

URGENT MESSAGE FOR ALL AGENTS: Decode using the standard V.A.L.A. decryption protocol. I want this matter resolved by the end of the day!  -- Herman T. Sherman, V.A.L.A. Bien (237)

And then the following cryptic message:

(913,38,869,134,5141); (1273,2209,3337,2881,391,1349); (1363,86,893,4331,2021,793,1927,583,142)

How much do they know? Have they figured out that your fake name is Jonah Orton, which is right there on the new recruit list? Should you escape now while you can? What's with the 237 at the end of the message? Could that be a clue to the decryption protocol? Can you decipher the code?

Save the Baby Kittens!

Congratulations, you passed the first math test! You sat through many propaganda lectures on the advantages of eating meat, how natural materials are better than synthetics, blah, blah, blah.

On your second day, Herman T. Sherman began the day thus:

Welcome to your second day of V.A.L.A. initiation. I see only about half of you are left--congratulations, you have the math skills to become a mission specialist! But that is only one of many skills you'll need. Another is the ability to kill quickly without hesitation. And tomorrow you will get the chance to kill a baby kitten with your bare hands! I will be making a fur coat with the pelts for my lovely wife Shirley, so you must not damage the coat. Good luck!

What? They want you to kill a baby kitten?! You must set the kittens free before tomorrow. After snooping around on your break, you heard adorable little meowing behind a locked door. The door has a lock on it but you found tiny lettering on one side which says:

• Reel B plus the last reel equals reel C
• The first reel time reel B is 54 more than reel D times the last reel
• Reel D times reel B equals 72

Can you figure out the lock combination and free the kittens before it's too late?

V.A.L.A. Initiation

V.A.L.A. Founder Herman T. Sherman

Congratulations, you figured out that the time it takes the sound to reach your ears makes a difference in your calculations for cliff height. While your partner works on the updated table, you have successfully joined V.A.L.A. as a new recruit! And you have a chance to get close to the founder. Not only is Herman T. Sherman in attendance, he's running the initiation process!

He began the initiation with this speech:

Welcome V.A.L.A. recruits. You are joining an elite group of villains that God himself has asked me to oversee. In many ways you are all like the ants in this ant colony, all working together for a greater good. But there is one way we humans are superior to ants and all the other creatures of this earth--and that is Math! A chimp does not know the factors of 237, but I'm sure all of you do. We are very careful here at V.A.L.A. To make sure you are right for V.A.L.A., please take out your pencils and scrap paper, clear your desks, and take this short math quiz.

One of his assistants then gave you a sheet of paper with these questions. You better get them all right or else you might be thrown out of V.A.L.A. on your first day!

Speed of Sound

Congratulations, you've uncovered the details of Operation: Agent Gerbil! You've left your palatial mansion and are now on your way to the Indian V.A.L.A. hide out. Your plan is to go undercover as a new recruit and take down V.A.L.A. from the inside!

On your flight to India, you suddenly realize that your calculations for determining cliff height by rock fall time are all wrong! You've forgotten to take into account the speed of sound which is 1,125 ft/sec. For example, if you dropped a 13 cm rock off a 1,125 ft cliff, your table tells you it will take 9 seconds to hit the bottom. However, it then takes another full second for the sound of it hitting the bottom to reach your ears! So the time you observe is 10 seconds!

Ignoring air resistance for now, make an equation that gives the time observed for a rock to fall, that is, the time it takes to fall plus the time it takes the sound to reach your ears (you can use t for time and x for the cliff height). Then use Wolfram Alpha to solve your equation for x which will give you the actual height of the cliff based on the observed time t. Use the equation to calculate corrected distances on your spreadsheet.

V.A.L.A. Minesweeper

Congratulations, you used your superior math skills to make a table that will tell you exactly how tall a cliff is based on how long it takes a rock to fall and how big the rock is. Even Galileo couldn't have done that calculation!

But now your vacation is over. Agents in training combed through the wreckage of the sunken 'W.A.L.A.' ship and found a backpack with a functioning tablet! V.A.L.A. has uploaded a new game--Minesweeper--to the tablet but so far none of the agents in training have been able to finish the game. Can you solve the puzzle to discover the next V.A.L.A. mission?

Mines left:

V.A.L.A. Reminder: Humans Good. Animals Bad.
 

Testing Galileo

Congratulations, you figured out how far a rock will fall each second assuming there's no air resistance (just like Galileo did):

• 1 sec = 16 ft
• 2 sec = 64 ft
• 3 sec = 144 ft
• 4 sec = 256 ft
• 5 sec = 400 ft
• 6 sec = 576 ft
• 7 sec = 784 ft
• 8 sec = 1024 ft

But how much difference does the air make? While soaking in your hot-tub next to your waterfall (see below), you decide to graph the velocity vs time for three different sized rocks up to 20 seconds. First graph the velocity in the absence of air (using 32 ft/s² for gravity). Next, add the velocity for rocks with 1 cm, 3 cm and 10 cm diameters. Use Wolfram Alpha to figure out the velocity by pasting in this equation:

v=sqrt(x)*tanh(sqrt(1/x)*9.8*t)*3.28

which gives the velocity in ft/s for t in seconds. The variable x is equal to 327*m/a where m is the mass in grams and a is the cross-sectional area of the rock in cm² (assume the rocks are spheres). Rocks weigh about 2.7 g/cm³. Once you have values of x for each size rock, you can use Wolfram Alpha to show the graph of velocity vs time. For example, for x =1000 you can enter this into Wolfram Alpha:

v=sqrt(x)*tanh(sqrt(1/x)*9.8*t)*3.28 where x=1000

To get the velocities after the first five seconds, you can use this:

v=sqrt(x)*tanh(sqrt(1/x)*9.8*t)*3.28 where x=1000, t={0,1,2,3,4,5}

How quickly do the different rocks slow down? Do you need to modify your table for the air resistance? Do you need different tables for different size rocks?

Calculate a new table for each size rock using this:

integrate sqrt(1000)*tanh(sqrt(1/1000)*9.8*t)*3.28 dt from 0 to 1

but replace '1000' with the value of x for each rock and the last '1' with the number of seconds the rock falls.

Relaxing at the Mansion

Congratulations, you sunk the boat and the torpedo! The threat to Staffa island has been eliminated for now and you deserve some rest and relaxation. While enjoying your mansion, you decided to watch a few Man vs. Wild episodes with Bear Grylls. In one of the episodes, he determined the height of a cliff by dropping a rock. He said that a rock falls about 50 feet for every second. But that doesn't seem right. The acceleration of the rock (at 32 feet per second per second) is a constant, but the velocity increases as it falls which means the distance per second increases over time. You decide to figure out how far a rock falls after each second up to five seconds. This will be a useful table of numbers to keep in your head while exploring.

Hints:

• First make a graph of the velocity vs. time, with velocity (in feet per second) on the y-axis and time in seconds on the x-axis
• To get the distance, you need to multiply the velocity (ft/s) times the time (s) which will give you the distance (ft) traveled during that time.
• Unfortunately, the velocity is changing over time, so which number should you use? Fortunately, your graph has the velocity at each time and the distance traveled is actually the area under the line because the area is also the velocity (y-axis) times the time (x-axis).

Torpedo in a Lifeboat

Congratulations, you successfully placed the explosive on the underside of the V.A.L.A. ship! The ship sank and everyone made it off safely. All the lifeboats started rowing east toward the Island of Mull. But then one lone boat veered off and is now headed toward Staffa island! You sent a quad-rotor over it for reconnaissance and you have spotted the torpedo in the boat! They must be trying to get closer and launch the torpedo from the small lifeboat!

You can see the boat is sitting low in the water due to the weight of the Mark 23 torpedo. That gives you an idea. If you drop sand into the boat, it should easily sink! The boat's capacity is 25 men. You assume the average man weighs 200 pounds, and you want to drop enough weight to exceed the boat's capacity by 10%. The sand on Staffa island weighs 130 pounds per cubic foot. How many cubic feet of sand should you drop on the boat to sink it?

Monkton's Salamander

Congratulations, you made it back to the A.A.K.V.O. yacht with just a few gallons of fuel to spare! You jetted off to Staffa island where a suspicious fishing boat is anchored several kilometers away. It is suspicious because there is a large torpedo on the deck and the front of the boat says W.A.L.A. but there is no fishing company with that name. The must be a V.A.L.A. ship!

You also just learned that not only is the Staffa Island cave a base for A.A.K.V.O., it is also a research station for Monkton's Salamander, a rare salt-water cave salamander discovered by A.A.K.V.O. founder, Monkton Tuesdale. You must save not only the base, but the salamanders too!

You plan is to sneak up on the ship and place an explosive under the water-line to sink it. You'll use your dive scooter to go the 4 kilometers from the island to the ship undetected. The scooter can pull you at 4 mph and you'll be travelling at 50 feet under the surface. You have a 130 cubic-foot tank. How much pressure should you put in the tank to make it to the ship and back with 200 psi reserve?  Hint: you might want to use this website. Hint #2: your RMV rate is 0.65 cu-ft/min.

Helicopter Fuel

Congratulations, you and your team figured out the combinations to all the locks and set all the slow lorises free! Now you need to get you and your crew to the A.A.K.V.O. ship waiting 200 km away off the coast in the Java Sea. You used up most of your helicopter fuel creating the hail storm that scared off the V.A.L.A. agents. Fortunately, the villains left a portable fuel tank at their camp. Unfortunately, there's only 110 gallons of fuel left. Your Bell-205 helicopter flies at 110 mph and gets 1.2 mpg. Do you have enough fuel to get back?

Combination Locks

Congratulations, your hail storm trick worked! The hail stones only lost 7% during their fall so they were still big enough. The remaining V.A.L.A. agents were freaked out by it and quickly left the island leaving the caged slow lorises behind.

Unfortunately, all the cages are locked with combination locks with four reels labeled 0 through 9. But what's the combination? As you examined one of the locks, you noticed very tiny writing on the back. With your A.A.K.V.O. magnifying glass, you were able to read the following:

• The 1st reel plus the 4th reel equals 3
• The 1st reel is a square number >0
• The 3rd reel plus the 2nd reel is 9 more than the 1st reel plus the 4th reel
• The 3rd reel plus the 4th reel equals the 2nd reel

Can you use the hints above to figure out the combination and free the slow loris?

Hail Storm

Your plan worked beautifully! The minions woke up this morning with lots of boils. They're miserable and packing up to go home. There is also a rumor going around that this plague of boils is a punishment by God because they are hurting animals—they don't suspect A.A.K.V.O. at all!

Unfortunately, there was one other camp of six V.A.L.A. agents separate from the main camp and they've been collecting Slow Lorises all day! You must save them but you don't want them to know that A.A.K.V.O. is responsible. Since they are already worried about plagues from God, you decide to give them another one: a Plague of Hail Stones!

You plan to drop golf-ball sized hail (2 cm radius) on the remaining V.A.L.A. agents from a helicopter 4 km up. Hail is very rare in the tropics so they will likely think it is another sign from God. It is hot in Java (30 °C) so you are worried about the ice balls melting before they can fall to the ground.What percentage will melt while they fall? How much bigger should you make them so they are golf-ball sized by the time they reach the ground?

Hints:

• You can get the velocity at which hail stones fall from this website.
• From that you can get the time they will take to fall in seconds
• The amount of heat lost (H) in Joules/second is H = C * A * (T2 - T1) where C is the coefficient of heat transfer (estimate from this website at 35 J/s*m²*°C), A is the surface area of the hail stone in m², T2 is the temperature of the air in °C, and T1 is the temperature of the ice in °C (in this case, the freezing temperature of water)
• Once you have the amount of heat lost in Joules/sec, you can calculate the total amount of heat lost in Joules during the fall
• It takes 333 Joules to melt 1 g of ice. You can now figure out how many grams of ice will melt during the fall
• From the radius of the hail stone, you can calculate the volume in cm³. Ice weighs 0.934 g per cm³ so you can calculate how much each hail stone weighs.
• Now you know how much each hail stone weighs and how much ice it loses during the fall. What percentage of ice is lost during the fall?

Save the Slow Lorises

Congratulations, you've discovered that V.A.L.A. will be attacking the A.A.K.V.O. base on Staffa island in the cave next to Fingal's Cave. But first you must save the Slow Lorises!

About one hundred agents and minions are camped out in the forest. You can see lots of hiking gear and dozens of empty cages waiting for captured slow lorises. They must be planning to spread out in all directions to search for slow lorises that they will then capture. They must be stopped!

There are too many of them for you and your crew of five to stop, but you can make them so miserable that they won't want to hunt for slow lorises. Your plan is to unleash thousands of Tomcat Beetles on the camp and induce a plague of boils similar to one of the biblical Plagues of Egypt. The beetles are attracted to the light and are active at dusk. Your plan is to surround the camp and unleash the beetles at the arrows marked below right at sunset so the beetles move toward the villains as they turn on their lanterns. You want to release enough beetles to cover one square meter with at least 10 beetles, but no more than that because you don't want them to spread to the nearby town. It is 60 m from the release point to the center of camp. How many beetles, rounded to the nearest thousand, should you and your agents each release?

Temple Instructions

Congratulations, you found the correct temple! Inside, you found a tube colored the exact same shade as the rock wedged in an upper corner of the temple. You pulled down the tube and inside was the paper to the right. It appears to give the location of the A.A.K.V.O. secret base they are planning to bomb and then raid. You copy down the numbers, put the paper back in the tube and then the tube back where you found it—you don't want V.A.L.A. to know you were there!

Now that you have the instructions, can you figure out which secret base they are targeting?

Prambanan Temple

Congratulations, you signaled the last A.A.K.V.O. plane leaving Greenland, and they rescued you! You have now arrived in Java. While spying on the V.A.L.A. minions setting up their camp, you overheard one of them tell another that the secret plans for bombing the A.A.K.V.O. base were hidden in the ancient ruins of the Prambanan Temple located about 100 miles to the east. You had one of your agents-in-training take the quad-rotor video below and then create a scale model of the temple site.



You heard them say the plans were hidden in one of the 224 small Pervara temples surrounding the main temples—but which one? You only heard them say that it was 10 grid units from the Shiva temple and 13 grid units from the Pervara temple closest to the southern Apit temple. What are they talking about? And which of the 224 small Pervara temples should you search for the secret plans?

Bear Island

You were on your way to Java from Greenland flying over the north Atlantic when you realized the gypsy psychic sabotaged your snow plane! She punctured the gas tank and you've been leaking gas ever since you took off. You had to make an emergency crash landing on Bear Island!

Your radio was broken in the crash and the gypsy also sabotaged your satellite phone. But you do have 120 meters of bright orange signaling cloth that you can use to make an S.O.S. signal. The last A.A.K.V.O. plane from Greenland should be coming in about an hour so you decide to set up your signal.

If you only have 120 m of cloth and want to use all of it to make the letters as big as possible, how high should the letters be if you arrange the cloth in the pattern below?

Kakuro 2.0 - Revenge Edition

Congratulations, you figured out the psychic was a fake using algebra! An urgent update has just been downloaded to the V.A.L.A. tablet: Kakuro Revenge! It sounds like the efforts of A.A.K.V.O. are finally getting to them. Solve the puzzle to find out the new orders!

V.A.L.A. Reminder: These tablets are for V.A.L.A. members only!   Copyright 2014 -- V.A.L.A. International