How many eggs are there in the basket? [closed]

There is a basket of eggs. The remainder is

• $1$ when we put the eggs in groups of $2$.
• $2$ when we put the eggs in groups of $3$.
• $3$ when we put the eggs in groups of $4$.
• $4$ and $5$, respectively, when we put the eggs in groups of $5$ and $6$.

How many eggs are there in the basket?

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closed as off-topic by heropup, 91500, user1551, Laurent Duval, tomaszJul 14 at 14:17

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – heropup, 91500, user1551, Laurent Duval, tomasz
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I see you've made at least 5 questions on this MSE, but you accepted only one of the answers given to you. You should accept your favorite answer. – Git Gud Jan 14 '13 at 16:13
@GitGud perhaps they were not suitable answers? – TheGreatDuck Jul 14 at 1:19
@TheGreatDuck If that's the case, my comment was unwarranted. – Git Gud Jul 14 at 22:30
@GitGud also, I have some pretty infamous questions with ten plus answers. No particular answer stood out, so I chose to not accept specifically because I wanted it to be clear that all the answers were equally sufficient, and equally engaging Tldr - not all questions can necessarily choose one answer to accept due to their nice diversity. – TheGreatDuck Jul 14 at 23:30
@TheGreatDuck I didn't want to fully explain the situation, but since you took the time to dissect this, let me do it too. Firstly, I take back what I said about my comment being unwarranted because I said the OP should accept their favorite answer - this is pretty obvious that they should do on the assumption that there is favorite answer, otherwise my comment talks about something which doesn't exist, it's meaningless. (Continues). – Git Gud Jul 15 at 17:59

3 Answers

Hint. If you have $n$ eggs, then $n+1$ is divisible by $2$, $3$, $4$, $5$, and $6$.

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59 eggs.

LCM of 2,3,4,5 and 6 is 60 which is divisible by 1,2,3,4,5 and 6. so if 1

is subtracted the required result is obtained which is 59. so at least

59 eggs is the answer.

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Good answer but please add more detail as to why subtracting 1 provides the appropriate number. Maybe point out that it is 59 + 60K as well, where k is any integer. - from first post review – TheGreatDuck Jul 14 at 1:21
@TheGreatDuck $k$ cannot be any integer, as $60 k + 59$ must be nonnegative (it's the number of eggs). – Rodrigo de Azevedo Jul 14 at 2:33
@RodrigodeAzevedo That kinda goes without saying... We are obviously talking about positive numbers here. – TheGreatDuck Jul 14 at 2:38

Since this question is over three years old, why not just give the solution? In Haskell:

λ take 10 $filter (\n->(rem n 2==1) && (rem n 3==2) && (rem n 4==3) && (rem n 5==4) && (rem n 6==5)) [1..] [59,119,179,239,299,359,419,479,539,599]  Hence, the number of eggs is in the set$\{ 60 m - 1 \mid m \in \mathbb N^+ \}$. What is so special about$60\$?

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