[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version="3.25"][et_pb_column type="4_4" _builder_version="3.25" custom_padding="|||" custom_padding__hover="|||"][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="3.27" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="3.27"]American Mathematical Contest 10A Year 2014[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="3.27" open="off"]Number Theory
[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="3.27" open="off"]7/10
[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="3.27" open="off"]Problem Solving Strategies Excursion In Mathematics
[/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]After having a long look into this problem you can first make attempt by listing the first few numbers of the given form.Give it a try!!!!!
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="3.27"]So we can do it like this 8*(8)=64 8*(88)=704 8*(888)=7104 8*(8888)=71104 8*(88888)=711104 Now try to observe the pattern in the above table because here lies the main insight of this problem . Come on cook it up!!!!!!
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.27"]So form the table you can observe the terms are following a pattern that's is The first number is 7 Then k-2 number of 1 Then the last two digits are 04
Now try to make the sum to 1000
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.27"]So now you are in the final part so you can easily find 7+04+(k-2)=1000
implies 11+(k-2)=1000 . Solving this equation we get the value of K is 991 which is the required answer.
[/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.[/et_pb_blurb][et_pb_button button_url="https://www.cheenta.com/matholympiad/" url_new_window="on" button_text="Learn More" button_alignment="center" _builder_version="3.23.3" custom_button="on" button_bg_color="#0c71c3" button_border_color="#0c71c3" button_border_radius="0px" button_font="Raleway||||||||" button_icon="%%3%%" background_layout="dark" button_text_shadow_style="preset1" box_shadow_style="preset1" box_shadow_color="#0c71c3"][/et_pb_button][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]