I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2013. Subjective Problem no. 4.
7.5 out of 10
[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book " open="off" _builder_version="3.23.3" title_text_shadow_horizontal_length="0em" title_text_shadow_vertical_length="0em" title_text_shadow_blur_strength="0em" closed_title_text_shadow_horizontal_length="0em" closed_title_text_shadow_vertical_length="0em" closed_title_text_shadow_blur_strength="0em"][/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="3.22.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px"]
Do you know what is Well-ordering principle ? it says that Every nonempty set A of nonnegative integers has a minimal element and a maximal element , which need not to be unique . now some time this simple property help us to get very nice solution to a problem , can you some how apply this property .
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="3.22.4"]Use the method of contradiction , first of all assume that there is no player which have the given property . Now try to use the property of hint 1 .
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.22.4"]If there is no such list , A's list has the maximum no. of players Now , if A does not have the certain property then there exist another another player B , who has won against A . Now B's list contain the name of A [ by the 1st condition ] and all the names of the players defeated by A [ by the 2nd condition]
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.22.4"]Now , can you find out some contradiction , yes exactly ..... B's list contain more number of element than A So, A's list must have the certain property .
[/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version="3.22.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px"]Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
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