معمای تیله ها

مجله تفریحی سرگرمی دخترونه

معمای تصویری, مسابقه تلوزیونی

تعدادی بچه مشغول بازی هستند. یکی از دوستانشان در حالی که کیسه ای در دست دارد از راه می رسد. هنگامی که سر کیسه را باز می کند، تیله های خوشرنگ از میان کیسه نمایان می شود.
 
اولین کودک، یک تیله و یک دهم تیله های باقیمانده مانده را بر می دارد.
کودک دوم، ۲ تیله و یک دهم تیله های مانده را بر می دارد.
کودک سوم، ۳ تیله و یک دهم تیله های باقیمانده را برای خودش بر می دارد.
به همین ترتیب تا کودک آخر (صاحب تیله ها) هر آنچه برایش باقیمانده بود را بر می دارد.
 
متوجه می شویم که همه این کودکان تعداد تیله های مساوی در دست دارند.

آیا می توانید بگویید در اینجا چند کودک وجود دارند و تعداد تیله ها چند تا بوده است؟

 

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جواب معما:
تعداد بچه ها را n فرض می کنیم و سهم هریک را از تیله ها برابر t و مجموع تیله ها را T در نظر می گیریم و قطعا خواهیم داشت: T=nt
— سهم کودک اول:

۱ + (T-1)/10 = t   ⇒  T = 10t – 9

 

— سهم کودک آخر: t

 

— سهم کودک یکی مانده به آخر:

n – 1 + t/9 = (T/t) – 1 + t/9 = t

 

با جایگزینی T خواهیم داشت:

۱۰t – 9)/t – 1 + t/9 = t

 

 

که می تواند به شکل زیر نوشته شود:

۸t2 – 81t + 81 = 0  ⇒  (t – 9)(8t – 9) = 0

 

از آنجایی که تعداد تیله ها نمی تواند کسری باشد، تنها جواب قابل قبول، t = 9 خواهد بود، و در نتیجه خواهیم داشت:  T = 81
بنابراین ۹ کودک مشغول بازی هستند و هر یک نیز ۹ تیله در دست دارند!

منبع:ihoosh.ir

مجلهتفریحیسرگرمیدخترونه

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