SOLUTION: When the eggs in a basket are grouped into 2,3, or 5 , there is always one extra. What is the least number of eggs for this grouping to be done?

Question 1044685: When the eggs in a basket are grouped into 2,3, or 5 , there is always one extra. What is the least number of eggs for this grouping to be done?
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
We can brute-force our way to a solution:
1 modulo 2 ===> 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29, 31
1 modulo 3 ===> 1,4,7,10,13,16,19,22,25,28,31
1 modulo 5 ===> 1,6,11,16,21,26,31
Barring the possibility that there is only one egg, the least number of eggs for this grouping to be done is 31.
(There is a conventional method of doing this problem, by means of the chinese remainder theorem, but the
solution above should suffice.)

Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
When the eggs in a basket are grouped into 2,3, or 5 , there is always one extra.
What is the least number of eggs for this grouping to be done?
~~~~~~~~~~~~~~~~~~~~~~~~~

Let N be the unknown number of eggs. Let us take one egg off. Then we will have N-1 eggs, and N-1 will be multiple of 2, 3, and 5. The least such a multiple is 2*3*5 = 30. Hence, N-1 = 30. Then N = 31.

Solved.

See similar problem in the lesson
    - The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9
in this site.

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