## 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