Counting eggs that leave remainders 1, 2, 3, 4, 5 in pairs, threes, fours, fives, sixes and none in sevens, under 150, gives:

1. Look for multiples of 7 that fit every condition. 2. Use the idea of LCM. 3. The answer is 119 eggs. _Source: syllabus Mathematics, Chapter 1, Real Numbers._