Can You Hunt For The Mysterious Numbers (II)?¶
Riddler Express¶
By all accounts, Riddler Nation had a lot of fun hunting for the mysterious numbers a few weeks back. So here’s what we’re going to do: For the next four weeks, the Riddler Express will feature a similar puzzle that combines multiplication and logic. We’ll be calling these CrossProducts.
For your first weekly CrossProduct, there are five three-digit numbers — each belongs in a row of the table below, with one digit per cell. The products of the three digits of each number are shown in the rightmost column. Meanwhile, the products of the digits in the hundreds, tens and ones places, respectively, are shown in the bottom row.
Can you find all five three-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 two 7s are fixed.
Step 2.¶
The 5 from 135 must be in 640. The 3 must be in 3,000 and the 9 must be in 3,969.
The 5s from 280 and 70 must be in 3,000. The 8 and 2 from 280 and 70 must be in 640.
Step 3.¶
The 5 from 45 and (an) 8 from 64 must be in 3,000 to complete the product.
45 must be 1·5·9, as 640 is not divisible by 3.
64 must be 1·8·8, as 3,969 is not divisible by 3.
Answer¶
