February 2018
Problem of the Month

De Morgan's Age Problem



This month's problem has two parts and is based on a statement made by Augustus De Morgan.   You must answer both parts correctly in order to get credit.

PART 1:
When asked about his age, the British mathematician Augustus De Morgan said,
"I was x years old in the year x2 ."

If De Morgan died on March 18, 1871, at the age of 64, for which years could he have made that statement?

PART 2:
When would a person living today have to have been born to make the following statement?
"I will be x years old in the year x2 ."



Solution to the Problem:

Part 1: De Morgan could have made that statement for 23 years:
1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858,
1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868,
1869, 1870, 1871

Part 2: A person would have to be born in 1980.

:
:
:

Examining a table of squares, you will find:

      x             x2      
      42           1764      
      43     1849
      44     1936
      45     2025
      46     2116


So, in part 1, the only answer that makes the statement true is age 43 in 1849.   Remember De Morgan died at the age of 64, so he wasn't alive in 1764.   Also, the statement is in the past tense, so the years that he could make that statement begin with the year of his death back to the year 1849.

In part 2, the only year that makes sense is 2025.   The person must be alive today (2018) and the statement is in the future tense.   So that eliminates 46 and 2116 because the person is not alive today (would have to be born in 2070).   It also eliminates 44 and 1936 because it would be in the past tense.   Therefore, the person must be 45 years old in the year 2025, so that person would have been born in 1980.




Correctly solved by:

1. Bryce Villanueva Victoria, Minnesota
2. Kelly Stubblefield Mobile, Alabama
3. Triniti Rogers Mountain View High School,
Mountain View, Wyoming
4. Ivy Joseph Pune, Maharashtra, India
5. Fabian Lorenz Graz, Austria
6. Brijesh Dave Mumbai City, Maharashtra, India
7. Clayton Price Ponce de Leon, Florida
8. Kimberly Howe The University of Alabama,
Tuscaloosa, Alabama


Honorable mention for answering one part correctly:

James Alarie Flint, Michigan
Paresh Chauhan Pune, Maharashtra, India
Sameha Haque Delta High School,
Delta, Colorado
Jonathan Punke Joliet Central High School,
Joliet, Illinois


Send any comments or questions to: David Pleacher