Question

Маша, Коля, Катя и Витя вместе нашли 12 белых грибов. Каждый нашёл хотя бы один белый гриб, и все нашли разное количество грибов. Маша нашла меньше всех, а Катя-больше всех. Сколько грибов могла найти Маша? Сколько Катя?

Answer 1

Катя - 1+ больше всех
Коля - 1+
Витя - 1 +
Маша -1+  меньше всех
Всего - 12 грибов

12 - 4 = 8(гр)
Если Маша всего 1гриб, то Катя 5 или 6 грибов
Если Маша 2 гриба, то Катя 4 гриба

Answer 2

#### Problem Analysis We are given that Masha, Kolya, Katya, and Vitya found a total of 12 white mushrooms. Each person found at least one mushroom, and they all found a different number of mushrooms. Masha found the fewest, while Katya found the most. We need to determine how many mushrooms Masha and Katya could have found. #### Solution Let's assume that Masha found **x** mushrooms and Katya found **y** mushrooms. From the given information, we can deduce the following: 1. Masha found fewer mushrooms than anyone else, so **x < y**. 2. Katya found more mushrooms than anyone else, so **y > x**. 3. The total number of mushrooms found is 12, so **x + y + z + w = 12**, where **z** and **w** represent the number of mushrooms found by Kolya and Vitya, respectively. We can rewrite the third equation as **x + y + z + w = 12** as **x + y + z + w - 12 = 0**. To solve this problem, we can use the method of trial and error. We will start by assigning values to **x** and **y** and then calculate the values of **z** and **w**. We will check if the conditions are satisfied, and if not, we will try different values until we find a solution that satisfies all the conditions. Let's start with **x = 1** and **y = 11**: - If Masha found 1 mushroom and Katya found 11 mushrooms, then the equation becomes **1 + 11 + z + w - 12 = 0**. - Solving for **z + w**, we get **z + w = 0**. - Since each person found at least one mushroom, **z** and **w** cannot be zero. Therefore, this solution does not satisfy the conditions. Let's try another set of values, **x = 2** and **y = 10**: - If Masha found 2 mushrooms and Katya found 10 mushrooms, then the equation becomes **2 + 10 + z + w - 12 = 0**. - Solving for **z + w**, we get **z + w = 0**. - Again, since each person found at least one mushroom, **z** and **w** cannot be zero. Therefore, this solution does not satisfy the conditions. Let's try one more set of values, **x = 3** and **y = 9**: - If Masha found 3 mushrooms and Katya found 9 mushrooms, then the equation becomes **3 + 9 + z + w - 12 = 0**. - Solving for **z + w**, we get **z + w = 0**. - Once again, since each person found at least one mushroom, **z** and **w** cannot be zero. Therefore, this solution does not satisfy the conditions. Based on the above analysis, we can conclude that there is no valid solution for this problem. It is not possible to determine the exact number of mushrooms Masha and Katya could have found given the given conditions. #### Conclusion Given the information provided, it is not possible to determine the exact number of mushrooms Masha and Katya could have found.