olymmath

Putnam 2021 A1

  • Session A

A grasshopper starts at the origin in the coordinate plane and makes a sequence of hops. Each hop has length 55, and after each hop the grasshopper is at a point whose coordinates are both integers; thus, there are 1212 possible locations for the grasshopper after the first hop. What is the smallest number of hops needed for the grasshopper to reach the point (2021,2021)(2021, 2021)?

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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