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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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48
Task/Babbage-problem/UNIX-Shell/babbage-problem-2.sh
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@ -1,7 +1,7 @@
#!/bin/dash
#!/bin/dash
# Babbage problem:
# What is the smallest (positive) integer whose square ends in the digits 269,696?
# What is the smallest (positive) integer whose square ends in the digits 269,696?
#
# He found the second to smallest number (99736 instead of 25264) using pencil and paper,
# and would not have wasted hours of computing time on his (planned) Analytical Engine (AE).
@ -47,38 +47,38 @@ done
a=1
# first workfile contains just the number 0
echo 0 >$wrk
echo 0 >$wrk
# test all workfile numbers with another digit in front
while test $a -lt $m # until the increment excees the modulus
do mm=$((a*10)) # modulus in this round
ee=$((e % mm)) # ending in this round
cat $wrk | # numbers from current workfile
while test $a -lt $m # until the increment excees the modulus
do mm=$((a*10)) # modulus in this round
ee=$((e % mm)) # ending in this round
cat $wrk | # numbers from current workfile
while read x
do y=$x # first number to test is the number read
while test $y -le $((x+mm-1))
do z=$(($y * $y)) # calculate the square
z=$(($z % $mm)) # ending in this round
if test $z -eq $ee
then echo $y # candidate for next round
fi
y=$(($y + $a)) # advance leftmost digit
done
done >$wrk.new # create new workfile
do y=$x # first number to test is the number read
while test $y -le $((x+mm-1))
do z=$(($y * $y)) # calculate the square
z=$(($z % $mm)) # ending in this round
if test $z -eq $ee
then echo $y # candidate for next round
fi
y=$(($y + $a)) # advance leftmost digit
done
done >$wrk.new # create new workfile
# next round
a=$((a*10)) # another leftmost digit
mv $wrk.new $wrk # cycle workfiles
a=$((a*10)) # another leftmost digit
mv $wrk.new $wrk # cycle workfiles
done
# find each number in the last workfile if x*x mod m = e
# ending in $e and modulus in $m
cat $wrk | # numbers from last workfile
cat $wrk | # numbers from last workfile
while read x
do y=$(($x * $x)) # check
do y=$(($x * $x)) # check
y=$(($y % $m))
if test $y -eq $e
then echo $x # solution found
then echo $x # solution found
fi
done |
sort -n | # numbers in ascending order
head -n 1 # show only smallest
sort -n | # numbers in ascending order
head -n 1 # show only smallest