All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Smudge Sludge (Posted on 2004-04-28) Difficulty: 3 of 5
   ??7
 x 3??
  ?0?3
  ?1?
 ?5?
 ?7??3
The above equation was written on a chalkboard to represent an example of a correctly answered multiplication problem. However, the class prankster went when the teacher wasn't looking and smudged many of the numbers. What did the original problem read?

See The Solution Submitted by Gamer    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution With Explanation Comment 9 of 9 |
(In reply to Answer by K Sengupta)

It is obvious from the respective last digits of the multiplier and the product that the last digit of the multiplicand must be 9.

Since 7*3(mod 10) = 1, it is obvious that the last two digits of the number at the third step is 51, so that the last two digits of the multiplier is 17.

Since 17*9 = 153, it is obvious that the first two digits of the number in the first step must possess the form 1(mod 9), so that the said first two digits can be 10, 20, ..., 90. of these, only 10 works, since 117*9 = 1053.

Thus, the number in the first step = 1053, and the multiplier = 117, giving the number in the third step as 3*117 = 351.

We now note that, the number at the second step consists of three digits with the middle digit being 1. considering all three digit multiples of 117, we observe that the middle digit of such a multiple can be 1, only when the number in the second step is 117, so that the multiplicand is 319.

Since the multiplier is 117 and the multiplicand is 319, we are now in a position to complete the muliplication as follows:

  117
x 319
------
 1053
 117
351
-----
37323

Edited on January 22, 2009, 1:23 pm
  Posted by K Sengupta on 2009-01-22 06:02:48

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information