Monday, July 5, 2010
(6 th July 2010)
1.A thought for a week
Imagination is more important than knowledge. Because knowledge is limited while imagination is unlimited. If knowledge is world,imagination will be universe, if knowledge is human, imagination will be divine,if knowledge is science,imagination will be arts, if knowledge is power, imagination will be super power,if knowledge is brutal king,imagination will be beautiful queen.
Hai friends, you might have enjoyed the recreational mathematics of last issue and multiplied further. With 3 successive even numbers,we have
2x4x6 + 4x4 = 4x4x4; 4x6x8 + 6x4 = 6x6x6 and in general 2n x(2n+2m)x(2n+4m) + (2n+2m)x4 = 8 (n+m)x(n+m)x(n+m).
Answer to the problem given in the previous issue
The sum of all the digits in a block number 142857 =R= 1+4+2+8+5+7= 27. The sum of 182 digits in the sequence = 30 R + last two numbers,i.e., 30 x 27 + 1 + 4 = 815;
125 th digit is (20 R + five)digit which ends with 5; sum 1000 = 37 x27 +1,i.e., the last digit of the sequence is 1.
The birthdate of my friend is 1 st April,but he knows only that I st January of that year is Sunday.Can you help him to find his birth day (if the year is not leap)
Sun(1)Mon(2)Tue(3)Wed(4)Thu(5)Fri(6)Sat(0).From Jan 1 to April 1 we 31+28+31+1=91
days;91/7 = 13R + 0.So it is Saturday. If the year is leap,it will be Sunday