Respected Sir / Mdm please go through this content. i hope its useful in teaching , Playing With Numbers of 8th Std Maths . With Regards Vijayeendra Purohit , Asst Master (PCM) G H S KALLAKAVATAGI 586114 , T&D Vijaypur * 9900878454 * HOW TO SOLVE A PUZZLE* (Courtesy : informguru.com)
*1. Preparation* Rewrite the problem, expanding the interlinear space to make room for trial numbers that will be written under the letters. For example, the puzzle SEND + MORE = MONEY, after solving, will appear like this: S E N D *9* 5 6 7 *+*M O R E *1* 0 8 5 *---------------* *M* O N E Y *1* 0 6 5 2 *2. Remember cryptarithmetic conventions* Each letter or symbol represents only one digit throughout the problem;When letters are replaced by their digits, the resultant arithmetical operation must be correct;The numerical base, unless specifically stated, is 10;Numbers must not begin with a zero;There must be only one solution to the problem. *3. See subtractions as "upside-down" additions* Ease the analysis of subtractions by reading them as upside-down additions. Remember that you can check a subtraction by adding the difference and the subtracter to get the subtrahend: it's the same thing. This subtraction: * C O U N T* * - C O I N* * ---------* * S N U B* must be read from the bottom to the top and from the right to the left, as if it were this series of additions: * B + N = T + C1* * U + I = N + C2* * N + O = U + C3* * S + C = O + C4* C1, C2, C3 and C4 are the carry-overs of "0" or "1" that are to be added to the next column to the left. *4. Search for "0" and "9" in additions or subtractions* A good hint to find zero or 9 is to look for columns containing two or three identical letters. Look at these additions: * * * * A * * * B* * + * * * A + * * * A* * ------- -------* * * * * A * * * B* The columns A+A=A and B+A=B indicate that A=zero. In math this is called the "additive identity property of zero"; it says that you add "0" to anything and it doesn't change, therefore it stays the same. Now look at those same additions in the body of the cryptarithm: * * A * * * B * ** * + * A * * + * A * ** * ------- -------* * * A * * * B * ** In these cases, we may have A=zero or A=9. It depends whether or not "carry 1" is received from the previous column. In other words, the "9" mimics zero every time it gets a carry-over of "1". *5. Search for "1" in additions or subtractions* Look for left hand digits. If single, they are probably "1". Take the world's most famous cryptarithm: * S E N D* * + M O R E* * ---------* * M O N E Y* "M" can only equal 1, because it is the "carry 1" from the column S+M=O (+10). In other words, every time an addition of "n" digits gives a total of "n+1" digits, the left hand digit of the total must be "1". In this Madachy's subtraction problem, "C" stands for the digit "1": * C O U N T* * - C O I N* * ---------* * S N U B* -- 1. If a teacher wants to join STF, visit http://karnatakaeducation.org.in/KOER/en/index.php/Become_a_STF_groups_member 2. For STF training, visit KOER - http://karnatakaeducation.org.in/KOER/en/index.php 4. For Ubuntu 14.04 installation, visit http://karnatakaeducation.org.in/KOER/en/index.php/Kalpavriksha 4. For doubts on Ubuntu, public software, visit http://karnatakaeducation.org.in/KOER/en/index.php/Frequently_Asked_Questions 5. Are you using pirated software? Use Sarvajanika Tantramsha, see http://karnatakaeducation.org.in/KOER/en/index.php/Why_public_software ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ --- You received this message because you are subscribed to the Google Groups "Maths & Science STF" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at https://groups.google.com/group/mathssciencestf. For more options, visit https://groups.google.com/d/optout.
