Занимательные задачи для детей «Логика»

zanimatelnaja-matematika

Логические задачи полезны как детям, так и взрослым. Мы предлагаем занимательные задания, над которым стоит подумать. Они направлены на детей старшего школьного возраста. Только логически рассуждая, вы сможете справиться с этими заданиями. Проверьте свои математические способности. Проведите интересно и с пользой свой досуг.

Задание 1. В вашем шкафу лежит 22 синих носка и 35 черных носков. Вам надо в полной темноте взять из шкафа пару носков. Сколько носков нужно взять, чтобы с гарантией получить совпадающую пару?

Задание 2.  Летит гусь. Навстречу ему — стая гусей. «Здравствуйте, 100 гусей», — говорит он им. Они отвечают: «Нас не 100 гусей; вот если бы нас было столько, сколько сейчас, да еще столько, да еще пол-столько и четверть-столько, да еще ты, вот тогда нас было бы 100 гусей». Сколько гусей летит в стае?

Задание 3. В зоопарке живут четвероногие звери и двуногие птицы. В зоопарке имеется 30 голов и сто ног. Сколько зверей и сколько птиц живет в зоопарке?

ОТВЕТЫ:

  1. Из шкафа нужно достать только три носка.
  2. Для решения этой задачи надо составить уравнение. Количество гусей в стае — это х. «Вот если бы нас было столько, сколько сейчас (т.е. х), — сказали гуси, — да еще столько (т.е. х), да еще пол-столько (т.е. 1/2х), да еще четверть-столько (т.е. 1/4x), да еще ты (т.е. один гусь), вот тогда нас было бы 100 гусей». Получается:

Произведем сложение в левой части равенства:

В стае летело 36 гусей.

3. Для решения этой задачи надо составить уравнение. Обозначим число зверей как х, а число птиц — как у. В зоопарке 30 голов, т.е. х + у = 30, и тогда х = 30 — у. В зоопарке сто ног, т.е. 4х + 2у = 100. Подставим в это равенство выражение х = 30 — у. Получим: 4(30 — у) + 2 у = 100. Преобразуем: 120 — 4у + 2у = 100 или 120 — 2у = 100, или 20 = 2у. Значит, у = 10, т.е. в зоопарке 10 птиц. А зверей в зоопарке: 30 — 10 = 20.

 

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