A Computer Randomly Prints Three-Digit Codes, with No Repeated Digits

question 115

Essay

A computer randomly prints three-digit codes, with no repeated digits in any code (for example, 387, 072, 760). What is the minimum number of codes that must be printed in order to guarantee that at least six of the codes are identical?

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Definitions:

Lube

Short for lubricant, a substance applied to reduce friction between moving parts in machinery or engines, extending their lifespan.

Geartrain Components

The individual parts that make up a geartrain, including gears, shafts, bearings, and casings, working together to transmit power in machinery.

Abrasive Contaminants

Hard particles or materials that can cause wear or scratching on surfaces they come into contact with, often found in working environments.

Machining Precision

The degree of accuracy and exactness in shaping parts by cutting, boring, drilling, or grinding, crucial for the proper functioning of mechanical systems.