Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 33323 by Rasheed.Sindhi last updated on 14/Apr/18

$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{If}{\mathrm{A}}_1,{\mathrm{A}}_2,...{\mathrm{A}}_{\mathrm{n}}\mathrm{are}\mathrm{n}\mathrm{points}\mathrm{with}\mathrm{integer}$$$$\mathrm{coordinates}\mathrm{of}\mathrm{a}\mathrm{plane}\mathrm{such}\mathrm{that}\mathrm{every}\mathrm{triangle}$$$$\mathrm{whose}\mathrm{vertices}\mathrm{are}\mathrm{any}\mathrm{three}\mathrm{of}\mathrm{the}\mathrm{above}$$$$\mathrm{points}\mathrm{has}\mathrm{its}\mathrm{centroid}\mathrm{with}\mathrm{at}\mathrm{least}\mathrm{one}$$$$\mathrm{non}-\mathrm{integer}\mathrm{coordinate}.\mathrm{Find}\mathrm{the}\mathrm{maximum}$$$$\mathrm{possible}\mathrm{n}.$$$$\mathrm{Recall}\mathrm{that}\mathrm{if}\mathrm{P}({\mathrm{x}}_1,{\mathrm{y}}_1),\mathrm{Q}({\mathrm{x}}_2,{\mathrm{y}}_2),\mathrm{R}({\mathrm{x}}_3,{\mathrm{y}}_3)$$$$\mathrm{are}\mathrm{three}\mathrm{vertices}\mathrm{then}\mathrm{centroid}\mathrm{G}\mathrm{is}$$$$(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3}{3},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2+{\mathrm{y}}_3}{3})$$

Commented by Rasheed.Sindhi last updated on 17/Apr/18

$$\mathrm{n}=972$$$$\mathrm{There}\mathrm{sbould}\mathrm{be}\mathrm{at}\mathrm{most}972\mathrm{points}$$$$\mathrm{in}\mathrm{order}\mathrm{to}\mathrm{meet}\mathrm{the}\mathrm{condition}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com