The set {1,2,...,10} is partitioned to three subsets A,B and C. For each subset the sum of its elements, the product of its elements and the sum of the digits of all its elements are calculated. Is it possible that A alone has the largest sum of elements, B alone has the largest product of elements, and C alone has the largest sum of digits?
Problem
Source: Baltic Way 2016, Problem 6
Tags: algebra
sahadian
28.03.2017 08:34
A={1,9,10},B={3,7,8},C={2,4,5,6}
mains_only
28.03.2017 08:52
sahadian wrote: A={1,9,10},B={3,7,8},C={2,4,5,6} C does not have the largest sum of digits.....
AHKR
28.03.2017 09:33
What is the meaning of sum of digits?
mains_only
28.03.2017 09:56
AHKR wrote: What is the meaning of sum of digits? Sum of digits means the sum of the elements (except for 10 , for which we would take the sum as 1)
AHKR
28.03.2017 11:23
Ignore..
RagvaloD
28.03.2017 12:30
sahadian wrote: A={1,9,10},B={3,7,8},C={2,4,5,6} A={1,9,10},B={2,4,5,6},C={3,7,8}
dogofmath
28.03.2017 19:33
Or A=3,7,10,B=2,4,5,6,C=1,8,9. Right?
mains_only
28.03.2017 20:03
dogofmath wrote: Or A=3,7,10,B=2,4,5,6,C=1,8,9. Right? Yeah this is also correct.....