Henry Ernest Dudeney/Puzzles and Curious Problems/163 - Domino Fractions/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $163$

Taking an ordinary box, discard all doubles and blanks.

Then, substituting figures for the pips, regard the remaining $15$ dominoes as fractions.

Arrange these $15$ dominoes in $3$ rows of $5$ dominoes so that each row adds up to $10$.

This gives us the equations:

$\ds \dfrac 1 3 + \dfrac 6 1 + \dfrac 3 4 + \dfrac 5 3 + \dfrac 5 4$

$=$

$\ds \dfrac {4 + 72 + 9 + 20 + 15} {12}$

$\ds = \dfrac {120} {12} = 10$

$\ds \dfrac 2 1 + \dfrac 5 1 + \dfrac 2 6 + \dfrac 6 3 + \dfrac 4 6$

$=$

$\ds \dfrac {12 + 30 + 2 + 12 + 4} 6$

$\ds = \dfrac {60} 6 = 10$

$\ds \dfrac 4 1 + \dfrac 2 3 + \dfrac 4 2 + \dfrac 5 2 + \dfrac 5 6$

$=$

$\ds \dfrac {24 + 4 + 12 + 15 + 5} 6$

$\ds = \dfrac {60} 6 = 10$