On my way to work, I pass by a digital thermometer outside a bank that
displays the temperature to the nearest integer, alternating
back and forth between Fahrenheit and Celsius at four-second
intervals.
The other day, when I was going to
work, I noticed that the temperatures displayed in
Fahrenheit and Celsius were simply reverse digits of each other.
Well, it warmed up nicely during the day, and
when I was on my way home, I looked at the same
thermometer.
Imagine my shock when, again, the
Fahrenheit and Celsius temperature displays were simply reversed digits of each other!
What was the temperature when I came in
to work, and what was it when I was on my way home?
Note: To convert from degrees Fahrenheit to Celsius, subtract 32 then multiply by 5/9. To convert the other way, simply do the opposite (multiply by 9/5 and add 32). Ignore leading zeroes.
By the problem, (c,f) =(10a+b,10b+a)(say)
Then, we must have:
10b+a=9(10a+b)/5 +32
=> 50b+5a = 90a+9b+160
=> 41b-85a=160
=> 41b=85a+160
=> b = 2a+4+((3a-4)/41) .......(i)
If a>=3, then, we must have:
b>= 10+(5/41)>9.
This is a contradiction as b as a digit must be <=9
Accordingly, a can only take the values 1 or 2( discarding a=0, since then c will be a single digit number.)
Substituting a=1 in (i) gives:
b=6-1/41, so that: b~ 6
Substituting a=2 in (i) gives:
b=8+2/41, so that: b ~ 8
Accordingly, (a,b)~ (1,6), (2,8), so that:
(c,f) ~ (16,61), (28,82)
Consequently, fhe same solution can be expressed in words in 2 ways:.
First Version: In the first instance the temperature was nearly 61 degrees Fahrenheit, which is approximately equal to16 degrees Celsius and in the second instance the temperature was nearly 82 degrees Fahrenheit which is approximately equal to 28 degrees Celsius.
Second Version: In the first instance the temperature was nearly 16 degrees Celsius which is approximately equal to 61 degrees Fahrenheit and in the second instance the temperature was nearly 28 degrees Celsius which is approximately equal to 82 degrees Fahrenheit.
Edited on December 22, 2021, 2:13 am
Puzzle Solution
