a 3 digit number is subtracted from a 4 digit number and the result is a 3 digit number. The 10 digits are all different.What is the smallest possible result ?
Answers
Answer:
420 can never be one of the three digit numbers, because then the 1's digit
of the other two numbers will be the same, and all the digits are different.
The possible 4-digit numbers are
1026 1062 1206 1602
1035 1053 1305 1503
1089 1098
Typical solutions from each 'family' are:
437 + 589 = 1026
289 + 764 = 1053
657 + 432 = 1089
You can switch digits in the same column between the three digit numbers,
and wherever there is no carry, you can switch columns.
And you can switch the two three-digit numbers entirely.
From those 3 solutions you can derive the others. In all there are 96,
including all rearrangements which are 'basically the same'.
Disregarding switches of the entire 3-digit numbers with each other, there are 48.
There are 32 (16) solutions in each family.
The smallest 3-digit number which appears is 246.
246 + 789 = 1035
The largest is 879
879 + 624 = 1503
Note that in all cases, the four digit number is divisible by 9.
1089 is also the solution to another famous problem of this type:
Take a 3-digit number with first and last digits different. 562 or 113 is ok, but 161 or 454 is not.
Reverse the digits and subtract the larger one from
the smaller one:
311 - 113 = 198
562 - 265 = 297
Then reverse the digits of the difference,
and add those two numbers:
198 + 891 = 1089
297 + 792 = 1089
The result will always be 1089
(because it is 11 * 99, and the intermediate number
is always a multiple of 99).
Hope it helps u and mark me as the brainliest answer