Random Thoughts: A Few Brain Teasers

Sharing some brain teasers I found interesting. See how many you can figure out yourself:

Problem 1: The Missing Dollar
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Image credit: Canvas

Three guests check into a hotel room. The normal charge for one night is $30, so each guest pays $10. Later the owner said that there's a promotion and the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.
Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?


Problem 2: Cut the Loss
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Image credit: iStockPhoto

One day a customer came to Tom's store. He collected $20 worth of merchandize, and then gave Tom a $50 bill. Since Tom didn't have enough change, he went to Charlie's store next door and exchanged the $50 bill into changes. Then he gave the customer $30 change. Shortly after the customer left, Charlie came to Tom and told him that the $50 bill was counterfeit money. So Tom immediately gave Charlie another $50 bill in exchange. So after all, how much money did Tom lose from this incident? Was it $50, $80, or $100?


Problem 3: Green Onion Vendor
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Image credit: The Virginian Pilot

A customer came to the green onion vendor and asked about the price of the green onions. The vendor said that the green onions sell for one dollar per pound. Since he had a total of 100 pounds, it would cost one hundred dollars to buy them all. The customer then asked if the vendor would consider selling green onion stems and leaves separately. The vendor told him that the green onion stems would sell for 70 cents and the green onion leaves would sell for 30 cents. The customer then decided to buy 50 pounds of green onion stems and 50 pounds of green onion leaves. The vendor then calculated as the following:


50 x 0.7 = 35, 50 x 0.3 = 15, 35 + 15 = 50

So the customer paid $50 and left. Now the green onion vendor was very confused: how come the customer was able to take away his $100 worth of green onions for only $50?


Problem 4: Find the Odd Ping Pong Ball
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Image credit: 123RF.com

You have 12 ping pong balls. One of them is slightly heavier OR lighter than the others. You also have a balance scale. How can you find the odd ball out, and if it is heavier or lighter, in only 3 weighings. Please help!


Problem 5: Silver Utensils Problem
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Image credit: Shutterstock

Bill wanted to buy some silver utensils, so he went to the utensil store and then found out that he only had enough money to buy 21 forks and 21 spoons, or 28 knives only. Since he needs to buy the same number of forks, spoons and knives to make complete sets, and he would really prefer to use up all the money he had brought, can you help him out?


Check out the answers to these problems here.



Video of the Day:

A great review of year 2011 based on what people searched in Google:

Random Thoughts: Sharing Some Mini-Stories

Sharing some mini-stories I read on the Internet. Hope you enjoy!

He was three when he peed his pants. She took her own pants off and gave it to him. "Remember to give it back to me," she said.
He was thirteen when he was courting a beautiful girl. She shoved her wallet into his hands. "Remember to give it back to me," she said.
He was thirty-three when he lost his ring. She took off the identical ring from her finger. "Remember to give it back to me," she said.
He was forty-three when the plane was about to crash. She strapped the parachute on him and waved. "You don't have to give it back to me this time," she said with a smile.

**********

Many years after the breakup they met again by chance.
Man: "How are you doing?"
Woman: "Good."
Man: "How is he doing?"
Woman: "Good."
"How about yourself?" the woman asked.
"Good."
Woman: "How about her?"
Man: "She just told me she is good."

**********

Everyday I would take the subway together with my girlfriend to go to work. Then one day and every day after she always found the handsome young man waiting for her outside of the station leaned on his sports car and looking at her with a big smile. At first she simply ignored him. But the handsome man and his sports car consistently showed up on time every day. Gradually she treated me with less and less enthusiasm until the day when the handsome young man confronted her with a large bouquet of red rose and asked, "Will you leave him, please?" "Of course!" she said with excitement. "She no longer loves you," the young man turned to me, "be my boyfriend, will you?" I accepted the bouquet.

**********

She climbed in the taxi and then recognized him. They had been intimate lovers ten years ago and had decided to go separate ways under the heavy pressure from their parents, never seeing each other again.
"How are you?"
"I am good, you?"
"Good."
She noticed the watch on his wrist was still the same one she had given him.
When she was getting off, he heard the jingles from the bell strapped on her handbag, the one he had given her.

**********

It was night. The boy had the girl on the back of his motorcycle.
Girl: "Can you slow down? I am scared."
Boy: "Isn't this fun?"
Girl: "Please! I am scared."
Boy: "Alright. Tell me you love me."
Girl: "Fine. I love you. Can you slow down now?"
Boy: "Can you take off my helmet and put it on. It's making me very uncomfortable."
The next day in the news: One death and one survivor in a motorcycle crash. Malfunctioning brakes to be blamed.

**********

In the United States.
"Hello...oh, hi mom, what is it?"
"Nothing, I just miss you."
"Alright, mom. I am really sleepy. It's early in the morning here. How many times have I told you. Don't forget the 12 hours timezone difference."
"Oh, I forgot. Go back to sleep..."
Five minutes later.
"Gosh, who's calling this early again!"
"This is your uncle. Your mom's apartment building is on fire!"
Dialing back immediately.
"Mom! Mom! Pick up the phone!!"
Ring...ring...ring...

**********

She works in a highrise building in the jungle of the city. He works in the office in the same floor just across the street. Everyday she would secretly watch him, imagining his joy and sorrow and then record them in her blog. Then one day he disappeared suddenly. She felt as if a chunk was missing from deep inside her heart. "He left. I miss him but he doesn't know." she wrote in her blog. A new comment quickly popped out. "Silly! I just moved to the floor above."

**********








Appreciate what you have before they are gone!

The Twelve Stances of Yi-Jin-Jing (The Tendon-Altering Sutra) Part 6

The Twelve Stances of Yi-Jin-Jing (The Tendon-Altering Sutra) Part 5

第十一式打躬击鼓

接上式，右脚落地，起身向右转90度，右脚向左脚收半步，距离与肩同宽，成下蹲势。 两手抬至头侧后方，掌心按压两耳，周身放松，中、食、无名指稍屈，轻轻叩击枕骨处，两手交替进行，各叩击七次，谓之”鸣天豉”。 鸣豉后双手抱后脑，缓缓向前弯腰，头垂于裆间至最大程度，膝挺直，如打躬状。 鸣天豉时身体先向左转90度，再向右转180度，再向左转90度。 弯腰垂头时牙关咬紧，作细微自然呼吸。 重复做三遍。

11^th Stance: Bowing Down and Beating the Heavenly Drum

Continue from the last stance. Put the right foot down to the ground and stand back up. Turn 90 degrees to the right to return to facing front. Move right foot half step toward the left foot so they are at shoulder width and then squat. Raise both hands above your head and then lower them behind the head until your palms cover your ears. Relax the whole body. Slightly bend the index fingers, the middle fingers, and the ring fingers and gently tap the occipital bone with alternating hands. Tap seven times with each hand. This is called “Beating the Heavenly Drum.” After beating the drum hold the back of the head with both hands and slowly bent forward until your head cannot go any lower between your crotches. Keep the knees straight as if you are bowing down. When beating the heavenly drum, turn your body 90 degrees to the left first, next turn 180 degrees to the right and then turn 90 degrees to the left. Clench your teeth while bending forward and take small breathes naturally. Repeat three times.

第十二势：掉尾势

两腿开立，双手仰掌由胸前徐徐上举至头顶，目视掌而移，身立正直，勿挺胸凸腹；十指交叉，旋腕反掌上托，掌以向上，仰身，腰向后弯，目上视；然后上体前 屈，双臂下垂，推掌至地，昂首瞪目。呼气时，屈体下弯，脚跟稍微离地；吸气时，上身立起，脚跟着地；如此反复21次。收功：直立，两臂左右侧举，屈伸7 次。

12^th Stance: Swinging the Tail

Stand with legs spread open. Slowly raise your hands past your chest and above your head, palms facing upward. Fix your stare on your palms as they move. Keep your body upright and don’t pull back shoulders or hold out your bosom. With ten fingers crossed, rotate your wrists and then lift upward with palms facing up. Extend the upper body and bend your waist backward while looking up. Then bend your body forward with both arms stretching out on the side and touch the ground. Lift your head and open your eyes wide. When exhaling, bend forward and at the same time lift the back heels off the ground slightly. When inhaling, return upper body back to standing position and land the back heels back to the ground. Repeat 21 times. To finish the exercise, stand in upright position and raise your arms from the side. Bend and extend the arms 7 times.

Again, please see how our friendly Mr. Bruce Wen demonstrate these two stances and explain things in English. Remember, Mr. Wen's version might be slightly different from the version I translated.

This concludes the entire Twelve Stances of the Yi-Jin-Jing. The following video shows a different flavor of the Twelve Stances of Yi-Jin-Jing demonstrated by a Shaolin monk in one smooth continuous form.

Video of the Day:

A National Geography documentary on the subject of Shaolin Kung Fu.

The Twelve Stances of Yi-Jin-Jing (The Tendon-Altering Sutra) Part 5

The Twelve Stances of Yi-Jin-Jing (The Tendon-Altering Sutra) Part 4

第九式青龙探爪

接上式，左脚回收于右脚内侧，成立正姿势。 左臂屈肘收回于左腰间。 同时右肘微屈，吸气，上体向左扭腰转体，右手向体前探爪抓去，并吐气发出“嘘”声，此时要求腰腹放松。 右手回收，向左46度方向做第二次探爪，再收回向左90度方向做第三次探爪。 然后，头带动躯干沿逆时针方向转动一小周，右手随之书一小圆（上图）。 两眼随右爪瞭望，如寻食状。 每次探爪均发出“嘘”声。 探爪时右臂一伸一缩，身体随之转后。 然后右手收回腰间，左手以同样动作向右探爪（下图）。

9^th Stance: Green Dragon Waving Its Claws

Continue from the last stance. Retract left foot back next to the right foot in an Attention position (like in military drills). Bend the left elbow and retract left arm next to the left side of the waist. Meanwhile, bend the right elbow slightly, inhale, turn the upper torso to the left, reach forward with the right hand in a dragon claw, exhale and make a “Shu” sound. Remember to relax the waist and abdomen for this stance. Retract the right hand back and then reach out the second time 46 degrees to the left with a dragon claw. Retract again and then reach out a third time 90 degrees to the left. Next, let the head lead the torso and make a small circular movement counterclockwise. Then make a circular movement with the right hand (see upper figure). Glance following the left claw hand as if hunting for preys. Make the “Shu” sound each time when reaching out with the claw hand. Extend and retract the right arm when executing the dragon claw. Turn your body afterwards. Then retract right hand back to the waist side and reach out with the left hand in dragon claw to the right (see lower figure).

第十式卧虎捕食

接上式，左臂回收于腹前，右脚向右跨一步，同时向右转体90度，上体顺势前倾，两掌手心向右前方下扑，如卧虎捕食。 此时两掌落地，成右弓步，昂首环视（上图）。 然后以双手手指支撑全身重量，左腿屈膝成90度，左脚抬离地面，脚心朝上﹔两臂一伸一屈，身体上下起伏。 做三至五次。 而后两手离地，手心翻向上，体向左后转180度，两手掌再翻向下，再做卧虎捕食动作，唯方向相反（下图）。

10^th Stance: Crouching Tiger Hunting for Prey

Continue from the last stance. Retract the left arm back to the stomach. Take a step to the right with the right foot and at the same time turn 90 degrees to the right. Lean the upper body forward following the natural flow of the movement and pounce forward with both palms facing down like how a crouching tiger pounces on its prey. Both palms should reach the ground while the legs are in a right front stance. Raise your head and look around (see upper figure). Next use fingers from both hands to support your entire body weight. Bend the left knee to 90 degrees and lift the left foot off the ground and turn the bottom of the foot upward. One arm should be in extended position while the other one is bent. Shift your body up and down for three to five times. Then raise both hands with palms facing upward and turn your body 180 degrees to the left. Turn the palms to face downward again and execute the crouching timer pouncing on prey move, only in opposite direction (see lower figure).

In the video below you can see our friendly Mr. Bruce Wen demonstrating these two stances and explain in English. Remember, Mr. Wen's version might be slightly different from the version I translated.

The Twelve Stances of Yi-Jin-Jing (The Tendon-Altering Sutra) Part 6


Picture of the Day: 

Although my 6-year old daughter Adeline has never learned the Tendon-Altering Sutra, although she is only a white belt, she certainly knows how to throw a beautiful kick!

10 Famous Thought Experiments That Just Boggle Your Mind Part 1

I ran into an interesting article in a forum (original in Chinese) that talked about 10 very famous thought experiments in the fields of philosophy, ethics, and psychology. Since I am getting a Doctor degree in Philosophy (hopefully), and also because I strongly believe these type of questions and experiments are very related in the research of artificial intelligence, I thought I'd share these with you together with my thoughts on the subject. Hope you enjoy!

10. The Trolley Problem

The trolley problem is a well known thought experiment in ethics, first introduced by Philippa Foot, a British philosopher. Trolley is the British term for a tram. The problem goes like this:

A trolley is running out of control down a track. In its path are five people who have been tied to the track by a mad philosopher. Fortunately, you could flip a switch, which will lead the trolley down a different track to safety. Unfortunately, there is a single person tied to that track. Should you flip the switch or do nothing?

A common answer takes the utilitarianism approach where flipping the switch becomes the obvious option because saving five lives result in a higher utility than saving just one life. But critics of the utilitarianism believe that flipping the switch constitutes a participation in the moral wrong, making one partially responsible for the death when otherwise the mad philosopher would be the sole culprit. An alternative view believes that inactivity under such a circumstance is also unethical. The bottom line: whatever you do, it is unethical. You are doomed either way.

It is reasonable to guess that your choice might vary if the single person happen to be your kid and the group of five consisted of four complete strangers plus your mother-in-law. In that case, you are simply assigning different utility values to different people (with the possibility of a negative utility). You no longer assume all people are equal. And if the group of five also included two other kids of yours, you simply assign the utility values and do the math and then make the "logical" decision (man, I am so cruel here!). This reminded me of a famous darn question people always get asked: if both your mother and your wife fall into the river and neither one knows how to swim, who should you save first? If you ever are asked this question, here's one answer you could use:

I'll jump into the river and drown myself, and we'll all go to heaven together. Now are you satisfied?

When it comes to artificial intelligence, a lot of times the choice is made based on a utility computation. Maybe the utility is computed using some fancy statistical functions. More advanced algorithms might take into consideration of probability or utility functions derived from past observations. Even more advanced algorithms might allow the agent to dynamically change or evolve the utility functions as time progresses -- a sense of learning. The agent will simply compute the utility values following whatever formulas it comes up with and then choose the option that will result with the highest utility. This is why AI agents or robots are normally considered to be very logical and at the same time very inhuman.It would be a long time before an AI agent would find itself trapped in this moral dilemma. (Remember the big computer in the movie War Games? It eventually figured out that the best winning strategy of playing the game of Tic-tac-toe was to not play the game at all).

So how would you design the AI agent or robot to be able to deal with morality, especially when you are giving it a weapon and grant it the permission to fire the weapon? Even we humans don't have clear clues in situations like in the Trolley Problem. Can we expect or require the agent or robot to do better than us? Unfortunately no one knows the right answer at the present time, we can only learn from our mistakes. Let's hope these mistakes are not disastrous and recoverable.

[Update on 8/2/2019]

Ten years have passed since I first posted this blog article. Today, many "self-driving" cars are already running on our roads (have you noticed those napping drivers in Teslas right next to you?), and there are only more to come with VCs and auto makers pouring money into this field. Now the Trolly Problem is becoming as real as it can be. When a self-driving car is faced with the dilemma of making a choice between killing the person on the left or four persons on the right, or even worse, when it needs to decide if it should sacrifice you, the passenger, in order to save four pedestrians, how would you feel about its logical choice? What if you are not the passenger, but the pedestrian, instead? Don't ask me. I don't have an answer.

Read Part 2: The Gettier Problem


Picture of the Day:

You can go here to see more animated portraits like this one.

BTW: The easiest way to remember my blog address is http://lanny.lannyland.com