Question

Ru has 100 jellybeans that she is placing in small boxes for a party game. She has decided that each box must contain at least one jellybean and no two boxes can contain the same number of jellybeans. As well, no box can go inside any other box. Determine the maximum number of boxes Ru can use for her jellybeans.

Answer 1

Ru will use 13 boxes.
You can either do 1+2+3+4+5+6+7+8+9+10+11+12+13 to get 91, and be unable of using the last 7, or, you can do 1+2+3+4+5+6+7+8+9+10+11+12+22 and use all 100. Either way, this will use 13 boxes

Answer 2

The maximum number of boxes Ru can use for her jellybeans is 13.

Calculus

Given that Ru has 100 jellybeans that she is placing in small boxes for a party game, and she has decided that each box must contain at least one jellybean and no two boxes can contain the same number of jellybeans, to determine the maximum number of boxes Ru can use for her jellybeans the following calculation must be performed:

• 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
• 55 + 11 + 12 + 13 + 14 = 50
• 55 + 50 = 105
• 14 - 1 (can be box of 5) = 13

Therefore, the maximum number of boxes Ru can use for her jellybeans is 13.

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