Just a multplication puzzle?

Question

In the following puzzle, 10 different letters are used, each representing a different digit from 0 to 9. (The underscores were added to get the columns to line up properly?) Can you reconstruct the multiplication problem?

_ _ _ P R S T
_ _ _ _ U V N
------------------
_ _ Y T T U X
X X V X X
------------------
X X N Z R U X

Answer 1

Firstly, V must be 0, otherwise, you would have had a third line while each of the three multiplications.

Now, we know that PRST * U = XX0XX. Now XX0XX = 11011 * X = 7*11*11*13*X, where X is a digit from 1 to 9.

Thus there aren't too many possibilities for PRST. It must be a multiple of 11*11*13 = 1573, since U is a single digit. It can't also be a multiple of 7, because that would make it >= 7*1573 = 11011. That means U must be a multiple of 7; thus U = 7, and PRST = 1573*X.

So PRST can be 1573, 3146, 4719, 6292, 7865, 9438. We can eliminate those which involve a 7 or a repeated digit: that only leaves 3146 (X=2) or 9438 (X=6).

Now we can just try the possibilities for N and see which gives an answer. The only one that matches the pattern is the second case where N=2, which gives:

_ _ _ 9 4 3 8
_ _ _ _ 7 0 2
------------------
_ _ 1 8 8 7 6
6 6 0 6 6
------------------
6 6 2 5 4 7 6

Answer 2

___9438
____702
-----------
__18876
66066
-----------
6625476

Key :

V=0

XX0XX = X * 11011

11011 = 7*11*11*13

Hence U=7 (U not equal X and 1 digit)
Also PRST = multiple of 11*11*13 = 1573

Greetings

Answer 3

i think u have a typo cause if T plus X equals R, and all of the numbers are less than ten then how can T plus X also equal Z?