-digit primes.Brittany : And the sum of your two uniform numbers is the date of my birthday earlier this month.Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.Ashley: And the sum of your two uniform numbers is today's date.What number does Caitlin wear?[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version="4.0"][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="4.0.9" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" _builder_version="4.0.9" open="off"]American Mathematical Contest 2014, AMC 8 Problem 23[/et_pb_accordion_item][et_pb_accordion_item title="Key Competency" open="on" _builder_version="4.0.9"]Basic knowledge about prime numbers , simple logical reasoning and number theory.[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.0.9" open="off"]6/10[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.0.9" open="off"]Challenges and Thrills in Pre College MathematicsExcursion Of Mathematics [/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="4.0.9" 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|0px|20px||" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]
, and the smallest two digit primes are 11,13,17. Now see that there are a few different sums that can be deduced from the following numbers, which are 
and 
, all of which represent the three days. So,the uniform numbers must be 11,13,17 otherwise there different sums will be more than 31 which gives a contradiction as the maximum amount of days any given moth can have is 31.[/et_pb_tab][et_pb_tab title="HINT 2" _builder_version="4.0.9"]Now we have to find which member has what uniform numbers from the given conversation .[/et_pb_tab][et_pb_tab title="HINT 3" _builder_version="4.0.9"] since Brittany says that the other two people's uniform numbers are earlier, so that means Caitlin and Ashley's numbers must add up to 
. Similarly, Caitlin says that the other two people's uniform numbers is later, so the sum must add up to 
. This leaves as today's date.[/et_pb_tab][et_pb_tab title="HINT 4" _builder_version="4.0.9"]From this, Caitlin was referring to the uniform wearers 
and 
, telling us that her number is 
, giving our solution as 11.[/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"]Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.[/et_pb_blurb][et_pb_button button_url="https://cheenta.com/amc-8-american-mathematics-competition/" url_new_window="on" button_text="Learn More" button_alignment="center" _builder_version="4.0.9" 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"]
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Caitlins number is 11