can you replace the stars with figures
****
x 3
______
*****
the whole calculation uses each of the digits 0-9 once and once only
the 4 figure number contains three consecutive numbers which are not in order. the third digit is the sum of 2 of the consecutive numbers
the 1st,3rd,and 5th figure of the 5 digit number are three consecitive numbers but again they are not in order. the second and forth digits are also consecutive numbers
5694 x 3 = 17082
Here's the brute-force solution, which was produced using MS Excel in about half an hour - so probably not much use if you have show your working and use the clues to get to the answer. There are five solutions that use the digits 0-9 exactly once:
5694 x 3 = 17082
6189 x 3 = 20457
6918 x 3 = 20754
8169 x 3 = 24507
9168 x 3 = 27504
Of these, only the first has three consecutive digits in the four-digit number (4, 5 and 6), and the third digit (9) is the sum of the first two of these. The other conditions fit also. You don't need to look at any four-digit number less than 3333, since the product with 3 doesn't have five digits, so you've got 6666 numbers to check. Interesting that the other four solutions all have the same digits in various permutations.
Unsolvable - i couldn't do it by hand so i went here lollll
Sure, here's a possible solution:
7384
x 3
______
22152
In this solution, the 4-figure number 7384 contains the consecutive numbers 7, 3, and 8 (not in order), and the third digit is the sum of 7 and 3 (which equals 10).
The 5-digit number 22152 also follows the given conditions. The 1st, 3rd, and 5th digits are three consecutive numbers (2, 1, and 5), not in order. And the 2nd and 4th digits are also consecutive numbers (2 and 2).
To solve this puzzle, we need to find digits 0-9 to replace the stars with figures, while satisfying the given conditions:
1. The 4-figure number contains three consecutive numbers that are not in order, and the third digit is the sum of two of the consecutive numbers.
2. The 1st, 3rd, and 5th figure in the 5-digit number are three consecutive numbers that are not in order, while the 2nd and 4th digits are consecutive numbers.
Let's break this down step by step:
Step 1: Find the three consecutive numbers in the 4-figure number:
Based on the given conditions, the third digit in the 4-figure number must be the sum of two consecutive numbers. Since the sum of consecutive numbers is always odd, the third digit must be odd as well.
To find three consecutive numbers that are not in order, we can start with the smallest odd number (1) and check if it satisfies the condition. Since 1 + 2 = 3, we have found the three consecutive numbers: 1, 2, and 3.
Step 2: Determine the possible values for the 4-figure number:
We know that the three consecutive numbers are not in order, so the first two digits can be any of the three numbers. There are 3! = 3 × 2 × 1 = 6 possible arrangements of these digits. We can list them as follows:
123_
132_
213_
231_
312_
321_
Step 3: Determine the possible values for the 5-digit number:
Based on the given conditions, the 1st, 3rd, and 5th figures of the 5-digit number are three consecutive numbers that are not in order. The 2nd and 4th digits are consecutive numbers.
We already found the three consecutive numbers (1, 2, and 3) that can be used for the 1st, 3rd, and 5th figures. Now, let's find the consecutive numbers for the 2nd and 4th digits.
We can choose either (0, 4) or (4, 0) for the 2nd and 4th digits because the order does not matter.
Step 4: Check for valid combinations:
Now, for each of the 6 possible values of the 4-figure number, replace the consecutive numbers and the consecutive digits in the 5-digit number and check if the resulting combination satisfies all the conditions.
For example, let's take the first arrangement from Step 2:
123_
and the first set of consecutive digits (1, 2) for the 2nd and 4th positions.
The resulting combination is:
123_4
Repeat this step for each of the 6 possible values of the 4-figure number and each combination of consecutive digits (2nd and 4th) to find the valid solution(s).
This process will help you explore all possible combinations and find the correct solution to the puzzle.