Alphametic puzzles — Part 2

 

(1)

(x, \; y, \; z)   are positive integers in arithmetic sequence such that

x \; < \; y \; < \; z,

z^3 \; - \; y^3 \; = \; TWO     and     y^3 \; - \; x^3 \; = \; TOW

Find   (x, \; y, \; z)

 

(2)

Substitute each of the letters with a different decimal digit from 0 to 9, to satisfy the following system of simultaneous modular alphametic equations:

one \; \equiv \; 1 \;  \mod{ \,two \,}
one \; \equiv \; 1 \;  \mod{ \,six \,}
six \; \equiv \; 0 \;  \mod{ \,two \,}

 

(3)

SWAN \; + \; MEDIC \; = \; IDIOM

Solve in base-10

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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6 Responses to Alphametic puzzles — Part 2

  1. pipo says:

    Puzzle one:
    (x, y, z) = (8, 9, 10)

    Puzzle two:
    581 ≡ 1 mod 145
    581 ≡ 1 mod 290
    290 ≡ 0 mod 145

    Puzzle three has many solutions, like:
    2437
    59168+
    61605

  2. pipo says:

    Oops you are right

  3. David @InfinitelyManic says:

    I see Pipo already posted a solution to #1
    8 9 10 271 217

    However if you want to know how to ACT like a CAT then:
    2 9 10 271 721
    ACT = 271
    CAT = 721

  4. pipo says:

    And if you want to know how she ACTS like two CATS then:
    7 12 17: 1385 and 3185
    ACTS = 1385
    CATS = 3185

  5. David @InfinitelyManic says:

    When PUPILS SLIPUP and hate math. I did not check for conditions in 2).
    100^3 -73^3 = 610983 = PUPILS
    73^3 -1^3 = 389016 = SLIPUP

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