$2.$ Heuristics

$($a$)$ Heuristic Admissibility The heuristic value for D$,$ h$($D$)$ has not been provided. What range

of values can h$($D$)$ have and satisfy the definition of admissible?

$($b$)$ Heuristic Consistency What range of values can h$($D$)$ have and satisfy the definition of consistent? $($Hint: apply the definition to all six arcs involving D and combine the resulting constraints.$)$

$3.$ Cryptarithmetic Consider the following cryptarithmetic problem:

O N E

$+$ O N E

T W O