If I have a 3 didgit number - a 3 didgit number = a 3 didgit number but the numbers used are 1-9 and only can be used once what are the numbers?
please help me i have been trying all week
impossible i reckon
surely not
There are lots of solutions, starting at
459 - 173 = 286
and ending at
981 - 746 = 235
perl code for the solutions:
for ($i = 123 ; $i <= 987 ; $i++) {
next if $i =~ /0/;
for ($j = 123; $j <= 987 ; $j++) {
next if $j >= $i;
next if $j =~ /0/;
$k = $i - $j;
next if $k =~ /0/;
next if $k < 100;
my %d = ();
$d{$_} = 1 foreach (split(//,"$i$j$k"));
my @d = keys %d;
next unless @d == 9;
print "$i - $j = $k\n";
}
}
not elegant, but does the job
To solve this problem, we need to find a three-digit number multiplied by another three-digit number that results in a three-digit number, while using the numbers 1-9 only once. Let's break down the steps to find the solution systematically:
Step 1: Determine the range of numbers to consider.
Since the question states that the numbers to be used are 1-9, we need to find three-digit numbers with unique digits from 1 to 9.
Step 2: Set up the equation.
Using the given information, let's set up the equation as follows:
ABC - DEF = GHI
Note: A, B, C, D, E, F, G, H, and I represent unique digits from 1 to 9, and each letter represents a specific digit.
Step 3: Analyze the equation.
We have three subtraction operations: A - D, B - E, and C - F. This means that the result of subtracting F from C should be greater than or equal to 0. Similarly, the result of subtracting E from B should be greater than or equal to 0. And finally, the result of subtracting D from A should be greater than or equal to 0.
Step 4: Find the possibilities.
Now, we need to find the possible combinations of the digits to meet the conditions mentioned above. Let's go through the different combinations:
First combination - A > D, B > E, C > F
Possible combination: (9 8 7) - (6 5 4) = (3 2 1)
Second combination - A > D, B < E, C < F
Not possible since we would end up with a negative difference.
Third combination - A < D, B > E, C < F
Not possible since we would end up with a negative difference.
Fourth combination - A > D, B < E, C > F
Not possible since we would end up with a negative difference.
Fifth combination - A < D, B > E, C > F
Possible combination: (6 5 1) - (9 8 4) = (2 7 3)
Step 5: Verify the solution.
By substituting the obtained values into the equation, we can check if the solution is correct:
987 - 654 = 333
651 - 984 = 273
So, the possible three-digit numbers that satisfy the given conditions are 987 and 654, yielding a difference of 333, as well as 651 and 984, yielding a difference of 273.