За­да­ча о пу­те­ше­ствен­ни­ке

При­ду­мал ко­гда-то за­да­чу. За­да­ча со­сто­ит из двух ча­стей, не тре­бу­ет на­пи­са­ния гро­мозд­ких фор­мул, и ре­ша­ет­ся про­сты­ми рас­суж­де­ни­я­ми.

Часть 1

По­сре­ди бес­край­ней плос­кой пу­сты­ни рас­по­ло­же­ны два го­ро­да: A и B (города́ мож­но счи­тать точ­ка­ми). В каж­дом го­ро­де есть ра­диопе­ре­дат­чик.

Пу­те­ше­ствен­ник вы­шел из го­ро­да A с це­лью до­брать­ся в го­род B. Что­бы не за­блу­дить­ся, он взял с со­бой един­ствен­ное сред­ство на­ви­га­ции: ра­дио­при­ём­ник, поз­во­ляю­щий пу­те­ше­ствен­ни­ку в той точ­ке пу­сты­ни, где он на­хо­дит­ся, при­бли­жён­но из­ме­рить уров­ни ра­дио­сиг­на­лов пе­ре­дат­чи­ков го­ро­дов A и B. Од­но из­вест­но точ­но: чем даль­ше пу­те­ше­ствен­ник бу­дет от­хо­дить от пе­ре­дат­чи­ка, тем мень­ший уро­вень сиг­на­ла бу­дет по­ка­зы­вать ра­дио­при­ём­ник, и на­обо­рот: чем бли­же к пе­ре­дат­чи­ку, тем боль­ший уро­вень по­ка­жет ра­дио­при­ём­ник.

Пу­те­ше­ствен­ник ни­где не оста­нав­ли­вал­ся и все­гда шёл так, что­бы уро­вень ра­дио­сиг­на­ла пе­ре­дат­чи­ка го­ро­да A не уве­ли­чи­вал­ся (со­от­вет­ствен­но, рас­стоя­ние до A не умень­ша­лось), а уро­вень ра­дио­сиг­на­ла пе­ре­дат­чи­ка го­ро­да B не умень­шал­ся (со­от­вет­ствен­но, рас­стоя­ние до B не уве­ли­чи­ва­лось). Од­на­ко че­рез не­ко­то­рое вре­мя пу­те­ше­ствен­ник по­нял, что боль­ше не мо­жет ид­ти та­ким спо­со­бом, а в го­род B он не до­брал­ся. Он оста­но­вил­ся и стал ду­мать.

По­ду­май­те и вы: в ка­ких точ­ках пу­сты­ни (от­но­си­тель­но го­ро­дов A и B) мо­жет на­хо­дить­ся пу­те­ше­ствен­ник? Ку­да ему нуж­но ид­ти, что­бы всё-та­ки дой­ти до це­ли?

Часть 2

По­ду­мав не­ко­то­рое вре­мя, пу­те­ше­ствен­ник осо­знал свою ошиб­ку и, по­няв, что ему на­до де­лать, до­шёл до го­ро­да B. По­быв не­ко­то­рое вре­мя в этом го­ро­де, он ре­шил вер­нуть­ся в го­род A. Пу­те­ше­ствен­ник ре­шил взять с со­бой дру­гой ра­дио­при­ём­ник, по­ка­зы­ваю­щий точ­ное рас­стоя­ние до го­ро­дов A и B. Пу­те­ше­ствен­ник до­га­дал­ся, что, ис­поль­зуя этот но­вый ра­дио­при­ём­ник, он смо­жет узнать своё ме­сто­по­ло­же­ние с точ­но­стью до зер­каль­ной сим­мет­рии от­но­си­тель­но пря­мой, про­хо­дя­щей че­рез го­ро­да. Это поз­во­ли­ло пу­те­ше­ствен­ни­ку за­ра­нее за­пла­ни­ро­вать свой марш­рут из го­ро­да B так, что­бы в кон­це марш­ру­та прий­ти в го­род A.

Пу­те­ше­ствен­ник вы­шел из го­ро­да B, од­на­ко судь­ба вновь ока­за­лась к не­му не­бла­го­склон­на: в пу­сты­не на­ча­лась пес­ча­ная бу­ря, и до го­ро­да A он не до­брал­ся.

Вам нуж­но ор­га­ни­зо­вать по­ис­ки пу­те­ше­ствен­ни­ка. К со­жа­ле­нию, он ни­ко­му не рас­ска­зал, ка­кой марш­рут он вы­брал. Из­вест­но лишь, что этот марш­рут по­стро­ен так, что­бы во вре­мя пу­те­ше­ствия рас­стоя­ние до го­ро­да B не умень­ша­лось, а рас­стоя­ние до го­ро­да A не уве­ли­чи­ва­лось. Опре­де­ли­те район пу­сты­ни (от­но­си­тель­но го­ро­дов A и B), в ко­то­ром пу­те­ше­ствен­ни­ка мог­ла за­стичь пес­ча­ная бу­ря.

128 отзывов на задачу

в пер­вом слу­чае он шел по окруж­но­сти с цен­тром в точ­ке Б, осо­знав ошиб­ку по­шел по ра­ди­у­су в сто­ро­ну уве­ли­че­нии сиг­на­ла от го­ро­да В.Во вто­рой ча­сти его марш­рут был по пря­мой меж­ду го­ро­да­ми
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