Book:Henry Ernest Dudeney/Puzzles and Curious Problems/Errata

Errata for 1932: Henry Ernest Dudeney: Puzzles and Curious Problems

$110$ -- An Absolute Skeleton: Solution

It can soon be discovered that the divisor must be $312$,

that $9$ cannot be in the quotient because $9$ times the divisor contains a repeated figure.

We therefore know that the quotient contains all the figures $1$ to $8$ once, and the rest is comparatively easy.

$112$ -- Simple Division: Solution

Divide $4,971,636,104$ by $124,972$, and the quotient is $39,782$.

$168$ -- Mental Arithmetic: Solution

Calling the numbers $a$ and $b$, we have:

$a^2 + b^2 + a b = \Box = /a - m b/^2 = a^2 = 2 a m b + b^2 m^2$.

$\therefore b + a = -2 a m + b m^2$,

$\therefore b = \dfrac {a \paren {2 m + 1} } {m^2 - 1}$

in which $m$ may be any whole number greater than $1$, and $a$ is chosen to make $b$ rational.

$174$ -- More Curious Multiplication: Solution

The number is $987,654,321$, which, when multiplied by $18$, gives $17,777,777,778$, with $1$ and $8$ at the beginning and end.

And so on with the other multipliers, except $90$, where the product is $88,888,888,890$, with $90$ at the end.

$176$ -- Counting the Loss: Solution

The general solution of this is obtained from the indeterminate equation

$\dfrac {35 x - 48} {768}$

which must be an integer, where $x$ is the number of survivors.

$188$ -- Squaring the Circle: Solution

The distance $DG$, added to the distance $GH$, gives a quarter of the length of the circumference, correct within a five-thousandth part.

$247$ -- The Counter Cross: Solution

There are $19$ different squares to be indicated.

Of these, nine will be of the size shown by the four $\text A$'s in the diagram, four of the size shown by the $\text B$'s, four of the size shown by the $\text C$'s, and two of the size shown by the $\text D$'s.

$254$ -- The Flanders Wheel: Solution

Move the counters in the following order: $\text {A N D A F L N D A F D N L D R S D L N A F R S E R S L N A L L}$ -- $30$ moves in all.