Nabila is smart! Nafiza smarter!!
Nafiza is a very funny girl!
She plays with numbers.
All her numbers are rational.
And she writes the numbers by p/q style.
Here both p and q are digits!!
Now her friend Nabila turns all the numbers written in p/q style into points.
Nabila writes them in the following way:
Here it’s ensured that before points there must be a zero. A,B,C,D,E and F are zero/nonzero digits!!
Now Nabila defines a function MULTmin , and declares MULTmin=A*B*C*D*E*F
And she finds all the MULTmin value of Nafiza’s numbers.
Then she tells one of her MULTmin value.
Hearing the value Nafiza understands what is the rational number chosen by Nabila.
HOW ? Find the way!
q can be 1 to 9
if q is 2,4,5,8, mult mn is zero as in those cases some of A,B,C,D,E,F, WILL BE ZERO.
IF Q IS 7 P IS LESS THEN 7 AND ANY NUMBER MULTIPLIED BY 142857 (1/7=0.142857) LESS THEN 7 HAVE SAME DIGITS.SO MULTI MIN FOR ALL 1/7 TO 6/7 WILL BE SAME (CYCLIC NUMBER).IF Q IS 9 THEN IT IS ALL ABOUT SIXTH ROOT AS 2/9 =0.222222…..
SIMILARLY FOR OTHERS.
IF Q IS 3 THEN IT CAN BE REPRESENTED IN 9 CASE AS 2/3=6/9 1/3=3/9
IF Q IS 6 THEN 2/6 IS SAME AS 1/3, 4,6 AS 2/3 3/6 AS 1/2 ONLY 5/6 IS .833333
SO THE MULTIMINN NABILA REFEREED WAS 8 *3*3*3*3*3 AS IT IS THE ONLY ONE BY WHICH WE CAN DIRECTLY IDENTIFY THE NUMBER
I FORGOT ABOUT 1/6 AND 1/9 IF MULTIMIN IS 1 THEN NUMBER WILL BE 1/9
AND IF IT IS 6^5 THEN IT IS 1/6 AS IT IS 0.166666
SO SHE WILL SEE IF MULTIMINN IS NOT SIXTH POWER OR FIFTH POWER OF A DIGIT THEN NUMBER WILL BE 5/6
OTHERWISE THOSE UNIQUE CASES ARE PREVIOUSLY MENTIONED
To write a fraction in the form p/q= 0.abcde. that is to ensure there is a zero before decimal q must be greater than p that is q>p.Now it we choose highest digit for q that is 9 then any number written in the form p/q or p/9 where p=1,2,…9 when converted to fraction attain the form p/9=0.ppppppp…
that is 1/9=0.11111
now after hearing the MultMIn value Nabila only need to find its fifth root to find the number.And to find the fifth root she only need to tell the last digit of the MultMin value .Because for every digit its fifth square ends in the same digit[assuming p and q are single digit numbers ]
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