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There are challenges specifically to MapReduce and then other challenges using Hadoop (which implements MapReduce) for developers, generally speaking.On the MapReduce side it is an entirely different thought process you need to have when attacking problems you need to solve. You are confined by a specific methodology and I have seen developers generally challenged being able to grasp the multi step process involved to chunk apart and re-group your data sets to solve a problem AND do so in a way that will work best.e.g. Lets say you have a data set that has super market purchases for the entire year for 1500 stores. Now lets say you need a total count of purchases from the entire year of Coke vs Pepsi. Developers when they first tackle MapReduce problems would Key on the data set in the Map phase for Coke and Pepsi in their Map sending those as the Keys to the Reducers... Now the problem is that the Reducers would then basically sit there and in only 2 loops count up the total for what it received. Sure, yeah this could work but really not so well with a lot of data and does not give you the benefit for using MapReduce. Instead it is better to key on lets say Coke+StoreID and Pepsi+StoreID. The Reducers would then have 3,000 Keyed Map results it could then sum simultaneously giving the developer a result that they then could do the final some in seconds and easily. The end result of the Reduce phase would be 3,000 rows with large total counts that can then get sumed using awk, Excel or if you want throw it in a db, whatever ... when the result set becomes large enough (millions, billions of rows in the data results) another M/R job is the way to go. Slice, Calc, Slice, Calc, Join, Calc, etc, etc.Now as far as what problems developers have with Hadoop I would say, generally speaking, it is deciding in what way they want to use MapReduce with Hadoop... There are many options!!!Going Java 100% is an option.Karmasphere http://www.karmasphere.com/ makes developer tools that help reduce the learning curve with Hadoop.Streaming is an option. The folks that choose streaming have the same similar problems across languages in regards to implementing MapReduce solutions in scripts using streaming. Languages like Ruby & Python have options for "toolkits" when doing streaming. Ruby has wukong https://github.com/mrflip/wukong) and Python has MrJob http://engineeringblog.yelp.com/2010/10/mrjob-distributed-computing-for-everybody.html and Dumbo https://github.com/klbostee/dumbo) that help abstract some of the nuances you can get caught up in when doing streaming. But you can handle challenge straight up in your scripts, not a problem (e.g. http://allthingshadoop.com/2010/12/16/simple-hadoop-streaming-tutorial-using-joins-and-keys-with-python/)Then there are options, like Hive and Pig, that sit "on top" of Hadoop abstracting most (arguably all) of the M/R complexities. So instead of writing Java jobs or streaming script Jobs that would be hundreds of lines and take hours ... instead simple as a few lines in a few minutes and it runs just as fast (in some cases even faster) as going the Java or streaming route.Lastely, Datameer http://www.datameer.com makes a "SpreadSheet" interface for Hadoop (completely abstracting away the M/R methodology and even the programming part) and running the jobs under the hood on Hadoop). Cool stuff!Hope this helps.

Assuming both knows the score of other only after the process is over, first lets see the 12 sided one's strategy, now expected number he will get is approx 7.85 like an american option, expected number in a turn is 6.5 so if he gets 1 to 6 in first roll he rolls it again otherwise notSimilarly if 1 to 10 for 20 side guyLet the 12one get r in his trials so 20 one should get r+1 or moreLet 12one be a and other be bSo because of the strategy followed by a the probability that he will get r belonging 1 to 6 is getting 1 to 6 in first turn and r(1 to 6) in second which cones out to be 1/24 (6/12*1/12) so getting 6 to 12 is 1/8 (sum of all prob is 1)Similarly for b 1 to 10 is 1/40 and 3/40 for the restNow if a gets r b gets r+1 or moreSo we divide r in 1 to 6, 6 to 10 and 11 and 121 to 6a(r).b(r+1 to 20)=sum 1 to 6 1/24*((10-r)/40+10*3/40)Explanation r in the given range has prob 1/24 for a each value and no of values for b is 20-r out which 10-r has prob 1/40 and 10 ha 3/40So the values is 219/(24*40)For range 6 to 10 by same logic1/8*((10-r)/40+3/4) suming 6 to 10We get 63/160For 11 121/8*3/40*(9+8) = 51/320Adding all three ans is 219/(24*40) + 63/160 + 51/320=750/960=25/32Hence probability is 25/32

In an isothermal process temperature remains constant.Consider pressure and volume of ideal gas changes from (P1, V1) to (P2, V2) then, from first law of thermodynamicsΔW = PΔVNow taking ΔV aproaching zero i.e. ΔV and suming ΔW over entire process we get total work done by gas so we haveW = ∫PdVwhere limits of integration goes from V1 to V2as PV = nRT we have P = nRT / VW = ∫(nRT/V)dVwhere limits of integration goes from V1 to V2on integrating we get,W=nRT ln(V2/V1) (3)Where n is number of moles in sample of gas taken.It may helps ……