There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there is one lily pad with no frogs on it. If each lily pad has exactly one frog on it, then there is a frog with no lily pad. How many frogs are at the pond?
Let's break down the information given step-by-step:
Step 1: If lily pads with frogs on them have two frogs each, then there is one lily pad with no frogs on it.
Step 2: If each lily pad has exactly one frog on it, then there is a frog with no lily pad.
Based on these steps, we can infer the following:
If there is one lily pad with no frogs on it, it means that all other lily pads have frogs on them.
If there is a frog with no lily pad, it means that there is one frog that doesn't have a lily pad.
From step 1, we know that each lily pad with frogs on it contains two frogs.
From step 2, we know that each lily pad can only have one frog.
Considering these inferences, we can conclude that there must be a contradiction in the given information. It is not possible to determine the exact number of frogs at the pond based on the information provided.
To solve this problem, let's break it down into two scenarios:
Scenario 1: Lily pads with frogs on them have two frogs each.
In this case, we know that there is one lily pad with no frogs on it. Since each lily pad with frogs has two frogs, we can determine the number of frogs by counting the number of lily pads with frogs and multiplying it by 2.
So, let's assume there are "x" lily pads with frogs on them. Therefore, the number of frogs in this scenario would be 2x.
Scenario 2: Each lily pad has exactly one frog on it.
In this case, we know that there is a frog with no lily pad. If each lily pad has exactly one frog, then the number of lily pads must be greater than the number of frogs. Let's assume there are "y" frogs at the pond.
Since there is a frog with no lily pad, and each lily pad without a frog has one frog on it, we can calculate the number of lily pads as "y + 1".
Now, to find the number of frogs in this scenario, we can simply count the number of frogs, which is "y".
To find the total number of frogs at the pond, we need to consider both scenarios together. The number of frogs will be the maximum value between the two scenarios. Therefore, the total number of frogs will be max(2x, y).
Based on the information provided, we do not have sufficient information to determine the exact number of frogs at the pond.
2(n-1) = n+1
n = 3
So, 3 pads, 4 frogs