This puzzle is designed for solving with a spreadsheet. Other
ways are possible, of course, but it makes a good spreadsheet
A man travels a prime number of miles in a prime number of
minutes at an average speed of 31 miles per hour (which is
another prime number).
Now that is not possible if all the figures are exact. Additional
information is that the figure for the miles travelled is exact
and the number of minutes is also exact, and both are prime
numbers. The figure for the average speed, however, is a rounded
number; i.e. the actual speed has been rounded to the nearest
whole number, which is 31.
What is the smallest number of miles for the length of the
ANSWER, and method of solution
The answer is 19 miles in 37 minutes.
You can see a spreadsheet diagram by scrolling down further
but you can construct it yourself as follows:
In column 1 make a series of odd numbers to represent miles . To
do this type "1" in cell A3 and use the Fill Down Series in
intervals of 2. This list includes all the odd primes. The
number two is also a prime number but is not the answer because 2
miles at 31 mph is approximately 4 minutes which is not a prime
number. Type the heading "miles" in cell A2.
In cell B2 type the heading "mins". In cell B3 compute the
minutes using the formula "=A3/31*60". Fill Down from this entry
to the same length as column 1. This gives a guide to the number
of minutes, although what we really need is a series of whole
In cell C2 type the heading "rounded mins" and in cell
C3 type the formula "=round(B3,0)". Fill Down as before. These
are the whole number minutes we will use.
Next we need to see the speed using the rounded minutes. Type
the heading "mph" in cell D2 and in D3 type the formula which is
"=A3/C3*60". Fill down as before. This column will start off
with the value 30 but not all the numbers will be integers.
We now need to see the rounded values of mph. Type the heading
"rounded mph" in cell E2 and the formula "=round(c3,0)" in cell
E3. Fill Down this column and you have the complete table.
All you have to do now is to inspect the table for the
required prime miles, minutes and "31" for the rounded mph. If
your table is like mine you will find the answer on line 12.
Here is a screen image I have made. All the numbers have been
set to "fixed" with three decimal places.
If you have any questions or problems about this, please email
me, David Broughton. My email address can be obtained by clicking
this symbol .
Who got it right?
I received 4 correct answers and one wrong one. The correct
answers were from John Stafford, Len Brent, Colin Rowe and John
Rackett. John Racket won the £5 book token in the draw.
The wrong answer was 41 miles in 79 minutes which was the next
pair of prime miles and minutes in the table, but the question
asked for the smallest. Thank you for all your answers.