Logic

Cryptograms

Cryptograms: Level 2 Challenges

         

XXYY+ZZXYZ \Large \begin{array} {c c c c } & & \color{#69047E}{X}& \color{#69047E}{X} \\ & & \color{#D61F06}{Y} & \color{#D61F06}{Y} \\ + & & \color{#3D99F6}{Z} & \color{#3D99F6}{Z} \\ \hline & \color{#69047E}{X} & \color{#D61F06}{Y} & \color{#3D99F6}{Z} \\ \end{array}

If each letter represents a distinct digit, what is the value of the three-digit number XYZ? \overline{XYZ}?

AB×AABAAB \begin{array}{ccccc} & & & & A&B\\ \times & & & & A &A \\ \hline & & B & A & A &B \end{array}

Solve the above cryptogram. What is the first two-digit number in the product above, AB\overline{AB}?

Note: A number cannot start with 0, so A and B are non-zero.

999×ABCDEF132 \begin{array} { l l l l l } & & & & & 9 & 9 & 9 \\ \times & & & & & A & B & C \\ \hline & & D & E & F & 1 & 3 & 2 \\ \end{array}

In this cryptogram, A,B,C,D,EA,B,C,D,E and FF are (not necessarily distinct) single digits. What is the value of A+B+C+D+E+F?A+B+C+D+E+F?

SEND+MOREMONEY \begin{array} { l l l l l } & S & E & N & D \\ + & M & O & R & E \\ \hline M & O & N & E & Y \\ \end{array}

In this cryptogram, each letter represents a distinct single digit positive integer except OO which is equal to 0. Find the value of MONEY.\overline{MONEY}.

ABCD×DDCBA \large{\begin{array}{cccccc} & & & A & B & C&D\\ \times & & & & & &D\\ \hline & & & D& C & B&A\\ \end{array}}

Given that A,B,CA,B,C and DD are distinct single digit non-negative integers satisfying the cryptogram above, find A+B+C+DA+B+C+D.

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