Entries were due by July 11. But the contest said nothing about what year they were due.

Mr. Day said his brother was a bit of a jokester and would have approved of entering the contest as a lark. The cards also had a sentimental value: Mr. Day recalled spending a lot of time in the game of “flipping” baseball cards with his brother.

“It was a sad time in my life,” he said of entering the contest. “It was really intended to be for a laugh.”

Then came the sleuthing: An internet search turned up the scores of the games from July 19, 1957: the Milwaukee Braves versus the New York Giants (the Braves won 3-1); and the Baltimore Orioles versus the Kansas City Athletics (the Orioles won 4-2).

He also found an updated address to send the entry and discovered Tony Jacobs, the vice president and general manager of global confectionery for Topps.

Mr. Jacobs had once worked for Life Savers, a connection to candy dating to Mr. Day’s childhood. Mr. Day grew up in Port Chester, N.Y., near the Life Savers factory and could tell the day of the week by the aroma coming from the plant. (Cherry was the flavor on Mondays, for example.)

In another coincidence, Mr. Day had a baseball card for a pitcher who had the same name as the Topps executive. The pitcher, Tony Jacobs, spent his entire career in the minor leagues except for playing in two major league games in 1948 and 1955. Mr. Day included the card and addressed the envelope to Mr. Jacobs with instructions to have it delivered to him before July 11 — a nod to the contest rules.

The scores were easy to find, but the five gum wrappers were not.

He headed to the post office, prepared to mail the entry without the wrappers, and found a grocery store next door that sold a “jumbo size” box of the gum, he said. A woman ahead of him on the checkout lane tried to pay for her groceries with a $100 bill but the cashier said she could not accept such a large denomination.