Alphametic puzzles — Part 3

 

(1)

PRO \; \times \; BLEM \; = \; ECONOMY

 

(2)

ODD \; + \; ODD \; = \; EVEN   in base b   (   b \leq 16  )

 

(3)

AERO \; - \; NEXT \; = \; EXIT
AERO \; + \; NEXT \; = \; RARE

No zeros appear in the solution.

 

(4)

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

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

y^4 \; - \; x^4 \; = \; NEWS
z^4 \; - \; y^4 \; = \; LESS

Find   (x, \; y, \; z)

Determine the possible four digit number(s) that represent   WELL

L   and   N   are nonzero digits

 

(5)

Substitute each of the letters by a different digit from 0 to 9 such that the sum of digits of each of these words

POIRE, \; OPERA, \; PORTE, \; TAPIS, \; ASTRE, \; PATRE, \; LOTUS, \; LISTE, \; LOUPE   and,   OUTRE

constitutes ten consecutive terms of an arithmetic sequence in ascending order

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

One Response to Alphametic puzzles — Part 3

  1. David @InfinitelyManic says:

    Re 4
    12 13 14 7825 9855
    13^4 – 12^4 = 7825
    14^4 – 13^4 = 9855

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