### Puzzle 42 Solution

The total number of sweets up to bag x is given by x(x+1)(x+2)/6. Using this formula, we equate:

x(x+1)(x+2)/6 < 42 million. ie x(x+1)(x+2) < 252 million. Without solving the cubic equation, we can estimate the value of x+1 by taking the cube root of 252 million, which gives us 631.6

Since x+1 < 631.6, the largest integer x value satisfying the above equation is 630. Hence Chork can pack 630 bags of gems in all.

Answer: 630

x(x+1)(x+2)/6 < 42 million. ie x(x+1)(x+2) < 252 million. Without solving the cubic equation, we can estimate the value of x+1 by taking the cube root of 252 million, which gives us 631.6

Since x+1 < 631.6, the largest integer x value satisfying the above equation is 630. Hence Chork can pack 630 bags of gems in all.

Answer: 630

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