Logan's Wacky Number Puzzle
During Practice for the upcoming MAO Competition, Logan decides to ask Sanjoy a Number Puzzle:
1.) "I am a number A. I am the largest two-digit prime number in base 10. I am the atomic number of an actinide."
2.) "I am a number B. I am the sum of three consecutive cubes. In addition I am a Kaprekar Number, and I am the atomic number of an actinide."
Find the Product of A and B.
The answer is 9603.
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1 solution
SIMPLE again: actinides range from 89 to 103 atomic weight so here itself we are defining a range ,the next restricting condition is the largest 2 digit prime: has to be 97 , clear cut elimination, now for B, we can't go for 5e3 as it leads to 125 so one cube has to be 4e3, 64 then trial and error of two steps with a restriction of <103 summation and that they are consecutive summation of cubes, leads us to 2e3+3e3+4e3= 99 <103 also the last restriction being 99 the kaprekar number , which makes it more interesting, that is 99 99 is 9801 and 98+01 is 99 , [there are more forms as well] hence 99 97 maketh 9603.