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.....