Henry Ernest Dudeney/Modern Puzzles/70 - The Solitary Seven

Modern Puzzles by Henry Ernest Dudeney: $70$

The Solitary Seven

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It is the first example I have seen of one of these missing-figure puzzles in which only one figure is given,

and there appears to be only one possible solution.

And, curiously enough, it is not difficult to construct this simple division sum.

For example, as the divisor when multiplied by $7$ produces only $3$ figures we know that the first figure in the divisor must be $1$.

We can then prove that the first figure in the dividend must be $1$,

that, in consequence of bringing down together the last $2$ figures of the dividend,

the last but one figure in the quotient must be $0$,

that the first and last figures in the quotient must be greater than $7$,

because they each produce $4$ figures in the sum,

and so on.

Historical Note

This puzzle was originally submitted to Henry Ernest Dudeney by a person identified merely as the Rev. E. F. O.

Dudeney then published it in The Strand Magazine.

Research is needed to determine which issue.

The uniqueness of the solution was proved at the time by Harold Revell.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $70$. -- The Solitary Seven
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Skeleton Puzzles: $144$. The Solitary Seven