Monday, June 9, 2008

[Kapi Regnum] Sunday Puzzle 2008/06/08

Crate Counting

A young lad named Petri has just recently become of age to begin working to help secure his family's future.

He finds work in a nearby storehouse which specializes in the delivery of fruit related products to other towns and cities.

His first assignment is to place a range of products into crates ready to be delivered to a town in the far north of the country.

With this been such a long trip he also needs to account for a thin layer of herbs on the inside of the crates to keep the fruit fresh for when it arrives in town.

Taking the measurements of the crates from the outsides he finds them to be approximately 20x20, and 30cm in height.Note that the crates themselves are three centimetres thick all around, and he has to leave 2cm in each crate for the Herbs.

This leaves 15x15, and 25cm in height.

He has Apples, Grapes and Nuts to fit into the crates.
The Apples measure 3x3x3.
The Grapes & Nuts measure 1x1x1.

He has 1400 Apples, 10500 Grapes, and 5400 Nuts to pack into Crates. All Crates must be packed separately with different fruits; These fruits cannot be cut in any way and must be packed whole.

Question: How many Crates does Petri need to pack all the fruit in?


for Apples : one crates can pack (15/3)x(25/3)=40 unit
for Grapes & Nuts :one crates can pack 15x25=375 unit

so the answer is 1400/40+10500/375+5400/375=78 Crates

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