Answer:
The least number of eggs that could have been in the basket is 301
Explanation:
The problem can be solved by finding the least common multiple (LCM) of the numbers 2, 3, 4, 5, and 6 and then adding 1 to get the smallest number that satisfies the given conditions. The LCM of 2, 3, 4, 5, and 6 is 60, so we can start by assuming there were 60 eggs in the basket. If we remove 2, 3, 4, 5, and 6 eggs at a time from the basket, we are left with 1, 2, 3, 4, and 5 eggs, respectively. However, if we remove 7 eggs at a time, there are no eggs left in the basket.
To find the smallest number of eggs that works, we can add 1 to the LCM of 2, 3, 4, 5, and 6 and check if it satisfies the given conditions. Adding 1 to 60 gives us 61. If we remove 2, 3, 4, 5, and 6 eggs at a time from a basket of 61 eggs, we are left with 1, 2, 3, 4, and 5 eggs, respectively. If we remove 7 eggs at a time from a basket of 61 eggs, we are left with 4 eggs, which means that 61 is not the answer.
We can continue this process by adding 60 to each subsequent number until we find the smallest number that works. Adding 60 to 61 gives us 121, but this number also does not work. Continuing this process, we eventually find that adding 60 to 241 gives us a basket of 301 eggs, which satisfies all the given conditions. Therefore, the least number of eggs that could have been in the basket is 301.