Copyright © 1997 by Paul Niquette. All rights reserved.
|f the mother's
age in the puzzle is written
as AB in decimal, she is 10 A
+ B years old, and her daughter is 10 B
+ A years old.
It requires little sophistication indeed to rule out...
As noted elsewhere,
the youngest two-digit age, is 10. The youngest
reversible two-digit age is 12, but that makes x
= 9, quite young for motherhood. Accordingly, the
youngest age for the daughter that will meet the
conditions of the puzzle is 13.
Reversiblity in ages will be observed
...exactly six more times, as called for in the puzzle.
It is easy to see that taking any
higher value of x will permit fewer
recurrences. The sophisticated solver will be able to
show that there are only 26 pairs of ages for mothers
and daughters that are reversible.
Here is the idle question asked in the Bonus Puzzle...
Is there a temperature in Fahrenheit degrees that can be converted to Celsius degrees -- by simply reversing its digits?The formula for converting Fahrenheit to Celsius is C = (5/9*(F -32). If we let C = 10 x + y and F = 10 y + x then solve for x = (41 y - 160) / 85. Of course, x and y are each required to be decimal ciphers: 1, 2, 3, ... 9.
By trial substitutions we find two solutions...
x = 1 ; y = 6 and x = 2 ; y = 8Thus...