Bash script - a puzzle - bash

Question

The script takes only one argument (call it n). It then alternately adds and subtracts each digit of the numbers from 1 through n.
For example:
n = 12
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 1 + 0 - 1 + 1 - 1 + 2
output: 5
#!/bin/bash
number=$1
result=1
if (( number == 1 || number == 0 )); then
echo
echo number: $number
echo
else
for (( i = 1; i < number; i++ )); do
if (( i < 10 )); then
if (( i % 2 == 0 )); then
let "result = result + i + 1"
else
let "result = result - i - 1"
fi
else
for (( i = 10; i <= number; i++ )); do
if (( i < 100 && i >= 10)); then
let "result = result - i/10 + i%10"
else
let "result = result - i/100 + (i%100)/10 - (i/100)%10"
fi
done
fi
done
echo
echo result: $result
echo number: $number
echo
fi
It works fine for ints 0 to 9, but for n>9 it gives the wrong answer.
Please correct my script and explain to me why it's behaving like this.
PS I'm new to bash scripting, so I'd love to see another solution to this puzzle
PPS I'm familiar to java
EDIT
I fixed the code, and it works correct now
#!/bin/bash
number=$1
result=1
if (( number == 1 || number == 0 )); then
echo
echo number: $number
echo
else
for (( i = 1; i < number; i++ )); do
if (( i < 9 )); then
if (( i % 2 == 0 )); then
let "result = result + i + 1"
else
let "result = result - i - 1"
fi
fi
done
for (( i = 10; i <= number; i++ )); do
if (( i < 100 )); then
let "result = result - i/10 + i%10"
else
if (( i % 2 == 0 )); then
let "result = result - i/100 + (i%100)/10 - (i%100)%10"
else
let "result = result + i/100 - (i%100)/10 + (i%100)%10"
fi
fi
done
echo
echo result: $result
echo number: $number
echo
fi

Answer 1

Ok this should work apologies that I miss-read the question earlier
number=$1
MATSTR="";
for((i=1; i <= number; i++)); do
MATSTR="$MATSTR$i";
done;
echo $MATSTR | sed -e 's/\(.\)\(.\)/\1-\2+/g' | sed 's/+$//' | bc
Explanation:
For loop to create string concatenating all numbers from 1 to the number.
sed statement replaces the every two digits with 1st digit minus second digit plus
sed removes any trailing plus
bc calculates the statement

Answer 2

Here's your original solution, but with bug fixes (in comments). It still won't work for number > 99, of course.
#!/bin/bash
number=$1
result=0 # Don't start at 1!!
if (( number == 1 || number == 0 )); then
echo
echo number: $number
echo
else
for (( i = 1; i <= number; i++ )); do # <=, not <
if (( i < 10 )); then # < 10, not < 9
if (( i % 2 == 0 )); then
let "result = result - i" # subtraction! Also, the +1 was unnecessary
else
let "result = result + i" # addition!
fi
else
if (( i < 100 && i >= 10)); then
let result=result-i/10+i%10
else
let "result=result-i/100+(i%100)/10-(i/100)%10"
fi
fi
done
echo
echo result: $result
echo number: $number
echo
fi

Answer 3

After misreading the question, (or the question being unclear), the answer took only minor adjustments. The sting solution is probably the simplest approach using modulo to togget +/-:
#!/bin/bash
declare -i num=$1
declare -i res=0
str=""
[ "$num" -gt 1 ] || {
printf "\n Error: invalid input. usage: %s int (greater than 1)\n\n" "${0//*\//}"
exit 1
}
for ((i = 1; i <= $num; i++)); do # create the string of digits
str="${str}${i}"
done
printf "\n Calculations:\n\n"
for ((i = 0; i < ${#str}; i++)); do # walk down the string adding/subtracting each digit
if [ $((i % 2)) -eq 0 ]; then
((res+=${str:$i:1}))
printf " res + %3s = %3s\n" "${str:$i:1}" "$res"
else
((res-=${str:$i:1}))
printf " res - %3s = %3s\n" "${str:$i:1}" "$res"
fi
done
printf "\n Final Result: %s\n\n" "$res"
exit 0
output:
$ ./puzzle.sh 12
Calculations:
res + 1 = 1
res - 2 = -1
res + 3 = 2
res - 4 = -2
res + 5 = 3
res - 6 = -3
res + 7 = 4
res - 8 = -4
res + 9 = 5
res - 1 = 4
res + 0 = 4
res - 1 = 3
res + 1 = 4
res - 1 = 3
res + 2 = 5
Final Result: 5