Pandigital products
Problem 032: Pandigital products
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.
The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.
Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
Solution:
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Explanation:
The main focus here was optimizing the pandigital testing. The rest is just looping over every possible number.
We can optimize the outer loop a little bit if we look at the possible multiplicands.
There are only 2 possibilities if we need 9 digits in our calculation:
- 1-digit number * 4-digit number = 4-digit number
- 2-digit number * 3-digit number = 4-digit number
| Interpreter steps: | 42 123 428 |
| Execution time (BefunExec): | 7.19s (5.86 MHz) |
| Program size: | 166 x 21 |
| Solution: | 45228 |
| Solved at: | 2014-09-22 |