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Letter to Editor
May 13, 1737
The Virginia Gazette
Richmond, Williamsburg, Richmond County, Virginia
What is this article about?
A letter to Mr. Parks provides a solution to a tradesman's weighing puzzle from Gazette No. 39, recommending weights of 1, 3, 9, and 14 pounds to total 27 pounds, and describes a general method using a geometric progression with a ratio of 3.
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Full Text
Mr. Parks,
Please leave to let the Tradesman (who proposed a Question in your Gazette, N. 39) know, that if he will divide his Weight of 27 Pound into the following Weights, they will serve his Purpose, viz. 1, 3, 9, 14.
To answer any Question of this Sort, let the least Weight be One Pound, and every other Weight be the double of the Sum of all the Weights less than itself, and One Pound more, as far as the Number proposed will admit; or let the Weights be in a geometrical Progression, beginning with Unity, the Ratio being Three.
Suppose 100 was the Number proposed, then the Weights will run thus, 1, 3, 9, 27, 60, the Progression being continued to the Fourth Term, and their Sum taken from the given Number, leaves 60 for the last.
Please leave to let the Tradesman (who proposed a Question in your Gazette, N. 39) know, that if he will divide his Weight of 27 Pound into the following Weights, they will serve his Purpose, viz. 1, 3, 9, 14.
To answer any Question of this Sort, let the least Weight be One Pound, and every other Weight be the double of the Sum of all the Weights less than itself, and One Pound more, as far as the Number proposed will admit; or let the Weights be in a geometrical Progression, beginning with Unity, the Ratio being Three.
Suppose 100 was the Number proposed, then the Weights will run thus, 1, 3, 9, 27, 60, the Progression being continued to the Fourth Term, and their Sum taken from the given Number, leaves 60 for the last.
What sub-type of article is it?
Informative
What themes does it cover?
Commerce Trade
Science Nature
What keywords are associated?
Weighing Puzzle
Tradesman Weights
Geometric Progression
Balance Scale
What entities or persons were involved?
Mr. Parks
Letter to Editor Details
Recipient
Mr. Parks
Main Argument
dividing 27 pounds into weights of 1, 3, 9, and 14 allows weighing any integer amount up to 27 pounds; generally, use weights in geometric progression starting with 1 and ratio 3.
Notable Details
References Gazette N. 39
General Method: Double Sum Of Previous Plus One, Or Powers Of 3
Example For 100 Pounds: 1, 3, 9, 27, 60