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A Royal Question (Posted on 2011-05-13) Difficulty: 2 of 5
    THY
×   CAR
────────
    THY
   GAZ
 RRZC
────────
 RTZTRY

On a 14067 60932 the 2841 (=k069) asked: "…Me, to pay for the fuel? What is this 51487 23069?"

Fellow floobers are requested to make sense of the above.

See The Solution Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

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Solution Analytical solution Comment 2 of 2 |
    THY
×   CAR
--------
    THY
   GAZ
 RRZC
--------
 RTZTRY

First, since THY×R=THY, R=1.

    THY
×   CA1
--------
    THY
   GAZ
 11ZC
--------
 1TZT1Y

In the penultimate column of addition, T cannot equal 1, so T must represent 2 and there is a carry digit from the next column.

    2HY
×   CA1
--------
    2HY
   GAZ
 11ZC
--------
 12Z21Y

Since there is a carry digit, G does not equal 0; rather, G is 9 and there is another carry digit from the next column:

    2HY
×   CA1
--------
    2HY
   9AZ
 11ZC
--------
 12Z21Y

From the second product, 2HY*A=9AZ, which is only possible if A=3 or A=4.

From the third product, 2HY*C=11ZC, which is only possible if C is 3,4, or 5.

From the second column of addition, neither H nor Z may represent 1, so H+Z=11, and there is a carry digit into the sum 1+2+A+C=10+2, which means A+C=9.

From these three facts, the only possible values of A and C are A=4 and C=5.

    2HY
×   541
--------
    2HY
   94Z
 11Z5
--------
 12Z21Y

From the third product, 2HY*5=11Z5, which is only possible if H=2 or H=3.

From the same product, Y must be odd (because the resultant product ends in 5).

Since 2 is already represented by T, H must equal 3. As the only other odd digit is 7, we have that Y=7, and by doing the mutliplication, Z=8.

    237
×   541
--------
    237
   948
 1185
--------
 128217

These are all the values in the equation, so we can plug those into the sentence:

On a RA06Y 60GHT the TZAR (=k06G) asked: "…Me, to pay for the fuel? What is this CRAZY TH06G?"

The only substitutions that make sense here are 0=I and 6=N, giving:

On a rainy night the tzar (=king) asked: "…Me, to pay for the fuel? What is this crazy thing?"

0=I
1=R
2=T
3=H
4=A
5=C
6=N
7=Y
8=Z
9=G

  Posted by DJ on 2011-05-13 21:49:21
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