Problem

A vexatious problem: each letter below stands for a different nonzero digit. What are the numbers?

sqrt(VEXATIOUS) = EEAAO

Solution

Thanks to Frederick Boehm:

The answer is sqrt(523814769) = 22887.

We first try to establish a value for E. Observe that 33112*33112 = 1096404544, a 10-digit number. Thus, E must be 1 or 2. Then note that 119982 = 143952004; since E is not equal to V, then E = 2. Next, we seek to narrow the range of V. Observe that 229982 = 528908004, while 221132 = 488984769. Thus, V=5. Then, we narrow the range for A. Observe that 227792 = 518882841, which means that A iseither 8 or 9. I then calculated the squares of 22881, 22883, 22884, 22885, 22886, and 22887 to reach the result 22887^2 = 52314769.

Correct Solutions

Michael Draper, Ian Zemke, Adrian Bernard (undergraduate); Dustin Moody, Aneesh Hariharan, Jacob Lewis, Gary Raymond (graduate); Frederick Boehm (postdoc); Marina Meila (faculty); Rich Bauer (alum) Navdeep Jaitly, Mattia Landoni (outside the UW)

Ian Zemke wins the prize!