BMAD Posted February 23, 2015 Report Share Posted February 23, 2015 Write a list from 1 to 100. Pick two numbers at random Sum the two numbers, find the product of the two numbers Sum the above two numbers Erase the two chosen numbers from the list Add the sum of the two numbers to the list Repeat until there is only one number. Repeat the above process multiple times. Is it the same number? Do the numbers center around a point? Bimodal? analyze. Quote Link to comment Share on other sites More sharing options...

0 gavinksong Posted February 25, 2015 Report Share Posted February 25, 2015 a ~ b = a + b + ab associativity: (a ~ b) ~ c = a ~ (b ~ c) => (a + b + ab) + c + c(a + b + ab) = a + (b + c + bc) + a(b + c + bc) => a + b + c + ab + ac + bc + abc = a + b + c + ab + ac + bc + abc The ~ is also obviously commutative. Thus, our number can be written unambiguously as 1~2~...~99~100. It is always the same number. Quote Link to comment Share on other sites More sharing options...

0 BMAD Posted February 24, 2015 Author Report Share Posted February 24, 2015 Hint... Try it for numbers 1-10 see what happens. Then try it for 1-20 and see what happens. Then generalize based on your conclusion. Quote Link to comment Share on other sites More sharing options...

0 BMAD Posted February 25, 2015 Author Report Share Posted February 25, 2015 anything else we can say about that number? Quote Link to comment Share on other sites More sharing options...

0 gavinksong Posted February 26, 2015 Report Share Posted February 26, 2015 Well, to be more explicit... the value is equal to the sum of the product of every subset of the operands. This can be seen somewhat intuitively if you interpret "a + b + ab" as "(all current terms) + (new operand by itself) + (all current terms appended with new operand)" Quote Link to comment Share on other sites More sharing options...

0 k-man Posted February 26, 2015 Report Share Posted February 26, 2015 anything else we can say about that number? For any 1...n sequence the result is (n+1)!-1 Quote Link to comment Share on other sites More sharing options...

## Question

## BMAD

Write a list from 1 to 100.

Pick two numbers at random

Sum the two numbers, find the product of the two numbers

Sum the above two numbers

Erase the two chosen numbers from the list

Add the sum of the two numbers to the list

Repeat until there is only one number.

Repeat the above process multiple times. Is it the same number? Do the numbers center around a point? Bimodal? analyze.

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