Can You Hunt For The Mysterious Numbers (V)?¶
Riddler Express¶
This is the fourth and final week of CrossProduct™ puzzles — for now. This time, there are four four-digit numbers — each belongs in a row of the table below, with one digit per cell. The products of the four digits of each number are shown in the rightmost column. Meanwhile, the products of the digits in the thousands, hundreds, tens and ones places, respectively, are shown in the bottom row.
Can you find all four four-digit numbers and complete the table?
Solution¶
Step 1.¶
First, list all possibilities of products of single digits. Products that are fixed are boxed.
The only 7 corresponds with 2,688 and 630.
384 is not divisible by 5, so the order of 125 is set.
960 and 384 are not divisible by 9, so the product and most of the order of 1458 is set.
The product and order of 630 is set.
Step 2.¶
The 6 from 2,688 must be a factor of 270. The product and order of 270 is set.
The order of 2,688 is set.
Step 3.¶
The remaining factors of 128 must be 8 and 8.
The remaining factors or 1,458 are set.
Answer¶
