## Contact

### Moscow

University Communications and Marketing

Fax: 208-885-5841

Email: uinews@uidaho.edu

U of I Media Contacts

# January 2023 Puzzler

## Question

It seems to have turned cold a bit early this year. Here’s a puzzle appropriate for the onslaught of winter.

A ball was floating in a pond when the pond froze. When the ball was removed it left a dent in the ice that is 6 inches deep and 20 inches across. What is the diameter of the ball?

## Solution to the September Puzzler

The angle X is 54 degrees. We’ll use the diagram shown here, in which points H and F represent my head and feet, while M and A are the tips of my morning and afternoon shadows. Here are some facts we can derive from the problem statement.

• First, segments FH, FM, and HA are all equal to my height.
• That makes triangles FHM and HFA isosceles.
• So angle(FHM) and angle(FMH) are equal.
• Both angle(FHM) and angle(FHA) are complementary to angles of size X, so we can now say that angle(FHM), angle(FMH), and angle(FHA) (all shaded yellow in the diagram) are all 90 – X.
• The angles of triangle FHM must add to 180, so angle(HFM) must be 180 – 2(90 – X) = 2X.
• That means angle (HFA) is 180 – 2X, and since triangle HFA is isosceles, angle(HAF) is also 180 – 2X.
• The three angles of triangle HFA must add to 180, so we get an equation:

2(180 – 2X) + (90 – X) = 180

270 = 5X

X = 54

### Correct Solvers:

First correct solution: Alex Blumenfeld, NMR Lab Manager, U of I Chemistry

Second correct Solution: Greg Stenback, B.S. Geological Engineering 1984, M.S. Statistics 1987

### About the University of Idaho

The University of Idaho, home of the Vandals, is Idaho’s land-grant, national research university. From its residential campus in Moscow, U of I serves the state of Idaho through educational centers in Boise, Coeur d’Alene and Idaho Falls, nine research and Extension centers, plus Extension offices in 42 counties. Home to nearly 11,000 students statewide, U of I is a leader in student-centered learning and excels at interdisciplinary research, service to businesses and communities, and in advancing diversity, citizenship and global outreach. U of I competes in the Big Sky and Western Athletic conferences. Learn more at uidaho.edu.

## Contact

### Moscow

University Communications and Marketing

Fax: 208-885-5841

Email: uinews@uidaho.edu

U of I Media Contacts