You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
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The problem: If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?
Now the 5L container contains (5 – (3-2))L or the desired 4L
I need to find a time to train other than the half hour open mat after karate. In combination with the summer heat, the cardio I have added to the workout leaves me wiped. I started doing rolls and was noticing jamming my shoulder a little bit because I was going “floppy” at the mid section. I am not going to count this day towards working out – after the rolls I went to start breakfalls and found I could not sit up from even a single back breakfall. Not cleanly anyway.
Time: 0
10 forward rolls
10 backwards rolls.
During karate I found I am heavier than anyone in the dojo by 25 pounds. I seriously need to get on my weight and suck back down to 180-190.
I got to try some ground work with Sensai Robles on tusday night. He hurt his neck and was wearing a t-shirt. This was eye opening as it meant there was no collar on his garment to grab onto. So collar chokes were out. Turns out chokes and strangles are most of my ground work which was an interesting discovery in and of itself and definitely something I need to work on. Since I had nothing to work with on above the wast I kept trying to get Sensai with a figure four ankle lock. Apparently I did a comical job of it because when we were done Sensai though I was trying for the achilles lock. He was giving me the benefit of the doubt – the Achilles Lock is a much better technique to go for from the position I kept working from.
The Achilles Lock is an ankle lock where the Radius of Nage’s arm is driven into the Achilles tendon of Uke. The technique is shown below from a seated position – but it looks like this technique can also be used from a standing position.
The figure below shows the bones and muscles of the lower leg. The Achilles tendon connects the calf muscles to the Calcaneus or heal bone. It sits behind the tibia.
Once Nage positions the radius of his forearm on the achilles tendon of Uke, he sets the technique by arching his back away from Uke. The set is similar in this respect to a seated arm bar. I need to talk to Sensai and ask him to show me ways to setup this technique – I tried this out on two different people at the dojo but just could not get into position to throw the technique.
The achilles tendon connects to one of the strongest muscle groups in the body. It can apparently take 2-12 times the persons body weight when running or jumping. That stress is translated along the length of the leg. Two common achilles injuries are when the achilles stretches or snaps. Since this technique applies force orthogonally to the tendon I am forced to wonder how likely it is to cause achilles injury when applied. If not a snap – certainly a stressing or strain.
This is more along the lines of proving what I know. Kind of struck me that this is a visual representation of something you see in martial arts all the time. You can use techniques you know to force your way through to a valid but un-elegant solution or you can do it elegantly. Both are technically correct but it is pretty obvious which way you should be solving the problem. *ugh* I think I am not up to reviewing though freshman year of high school. Who would have thought I forgot so much.
Got a half hour of open mat time after Karate.
10 forward rolls
10 backward rolls
10 Nikyo-undo
10 Sankyo-undo
10 Kote-Gaeshi-undo
20 Tekubi-kosa-undo, Tekubi-joho-kosa-undo -> Still not getting these right. Weight not staying under side.
10 Ikyo-undo
10 Zengo-choyaku-undo
10 Fune-Koki-Undo
10 Koho-Undo
10 Ushiro-undo
I was having problems with Zengo-choyaku-undo where my line kept drifting so I drilled just the footwork for 5 mins.
This problem is representative of a class of problems that I can solve – but only thought brute force. In some cases – like this one – I can winnow my guessing spaces though the use of logic and algebra – but it is still a brute force attack. What I don’t see is how to make a non-brute force algorithmic attack on this problem.
This problem was phrased with five rectangles tiled to cover a square – with a much larger number of squares I could not easily do it by hand and if I was to write a program to do it that attack would also be brute force.
Ugly as it is – here is how I solved this problem.
I just looked at the Mathproblems.info site where I saw this problem and they show three more solutions. One more with side length of 13 and two more with side length of 11. I was less thorough with my search of the 11 options and stopped on 13 after I found the first solution but the techniques seem to be the same for all solutions. Still brute force-ish though. There must be a better way to formalize solving this type of problem.
Problem #96 from Mathproblems.info (at http://mathproblems.info/group5.html) was one I have seen before as a kid :
“Three people (A, B, and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. There is also a bicycle available and any person can cross the bridge in 1 minute with the bicycle. What is the shortest time that all men can get across the bridge? Each man travels at his own constant rate.”
When I saw this problem as a kid there was the caveat that only one person could cross the bridge at any one time. For that case the fastest solution is to have
(1) A crosses with the bicycle. (2) C crosses. (3) C crosses back with the bicycle. (4) B crosses with the bicycle. (5) C crosses. This makes for a total crossing time of (1+2+1+1+2) or 7 mins.
The two new twist that the Mathproblems.info guys put on the problem was to remove the restriction that only one person could cross at a time, and allowing the bike to be left anywhere on the bridge. I am still working on this new version of the problem.
Sensai taught this technique last thursday (May 28th) – unfortunately I did not write it down right away and now that I sat down to capture it the details are fuzzy. The technique is a reversal, starting from a bottom position nage escapes the mount and puts uke in an arm-bar. The figure shows Nage putting an arm bar on Uke’s right hand
Step one
To start the technique Nage captures Uke’s right hand – immobilizing it on his chest with his left hand. If Uke is setting up Nage for a technique that starts with a lapel grab – like a deep collar choke – that lapel grab sets up Uke for the technique. So this technique should make for a counter.
As part of setting the escape up Nage makes sure the leg on the side he is arm baring is on Uke’s hip or higher. So if Nage is arm-barring Uke’s right arm then Nage’s right leg is on Uke’s left hip as shown in the figure.
Step two and three
Nage wants to rotate under Uke. Nage does a hip out under Uke. At the same time Nage hooks Uke’s inner thigh with his right hand. This hook lets Nage spin under Uke as opposed to the escaping movement a normal hip out would cause.
Step four
Nage raises his outer leg and hooks it over Uke’s neck. Since Nage still has Uke’s arm immobilized Uke is basically a tripod and unstable. So with Uke’s head hooked Nage can flip Uke over onto his back with just the leg hook.
Step five
Uke’s shoulder and torso should be touching Nage’s rear, if it is not Nage may have to slide his body forward. Uke’s arm runs through Nage’s groin with Uke’s upper arm resting on Nage’s pelvic bone. Nage’s hip forms the base of a fulcrum formed by Uke’s arm so it is important that the arm is resting on the hip bone and prevented from moving side to side by being sandwiched between Nage’s Legs. Nage sets the technique by arching his hips into the technique – this applies force on the joints using Uke’s arm as a leaver.
The seated arm bar is a joint technique executed on both the shoulder complex and elbow. So the arm needs to be straight so the technique locks out both the elbow joint as well as the shoulder.
Ok, so I just ground through this solution long hand – which sucks because I am fairly sure there was some slick trick I was supposed to have seen here. All the problems in this book are searching for an elegant solution and this one is anything but. I should ask Konrad what I missed when he gets back.
…. and it keeps going, and going, and going…. I am really missing something here. This will give me the right solution but *ick*.
