MAGICAL ADDITION.

The following is a peculiar arrangement of the figures 1 to 9, so that by adding them together they amount to 100:—

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100

To find the sum-total of three lines of figures upon the first line being shown, let any one write down a row of figures, and suppose they are 76854. Then take the paper, and, leaving space for two more rows of figures, say that the result of the addition of that row with two other rows can be given, the first of which rows may be written by any one present. Proceed by deducting 1 from the final right-hand figure, and place the figure 1 on the left-hand side; let the top row be folded over, and the paper handed back for the second row to be written, which we will suppose to be 34721; fill in the third row by making each figure in the second row up to 9 by writing 65278; the figures given according to the instructions will be the addition of the three rows.

76854

34721

65278

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176853

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The addition of five rows of figures may be told in a similar manner. Let any one present write down, as before, a row of figures, and then the calculator may undertake to tell the addition of that row with four other rows, two of which may be written by any person or persons present. This is attained by deducting 2 from the unit figure, and placing the figure 2 on the left-hand side. For example: again suppose the first row to be as before (76854); the result of the addition of that row and four others may be made to be 276852. After the first row has been written, fold it over, and request some one to write a second row of figures, which shall be supposed to be 34721; to this the magic calculator should write for the third row such figures as will make each of the above up to 9, namely, 65278; again, let a stranger write the fourth row, first turning over so as to conceal the second and third rows; whatever appears for the fourth row must be in each figure, as before, for the fifth row, made by the calculator to 9. Thus, if the fourth row be put down 80765, the necessary figures to add for the fifth row will be 19234, when the previously given total will be found to be correct.

76854

34721

65278

80765

19234

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276852

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In the last two examples of Magical Addition the only stipulations needed are that no subsequent row shall contain more figures than are contained in the first row, and that the first row shall end neither with a 1 nor a 0.