Constraint Satisfaction Problems $1(5$ points$)$

You are a customer and would like to exchange your $$50$ bill into smaller bills of $$1,$$$2,$$$5,$

and $$10,$ denoted by the variables ONE, TWO, FIVE, and TEN, respectively. For the

exchange, you would like strictly more than two bills of $$1.$ Further, you want the number of

$$2$ bills to be different from the number of $$1$ bills. The number of $$5$ bills is exactly four,

and the number of $$10$ bills is less than three. The domain for each variable is $[1,4].$

a$.$ What are the unary constraints? $(1$ point$)$

b$.$ What are the binary constraints? $(1$ point$)$

c$.$ What are the $n-$ary $(n>2)$ constraints? $(1$ point$)$

d$.$ Draw a $($hyper$)$graph of the constraint satisfaction problem. Indicate variable nodes

with circles and constraint nodes with squared nodes. $(2$ points$)$

$(2$nd image$)$

Program. Use Code Listing $1$ as a basis and complete the lines below $\%$ ADD

DOMAINS and $\%$ ADD CONSTRAINTS. First, define the domain for the variables

using the 'ins' operator. Then add the constraints using the operators $($#$>,$ #$>=,$ #$=,$

#$=,$ # # to define the inequalities and equalities. Write each constraint on a

separate line, ending in a comma $(,),$ except for the last constraint which ends in a

dot $\text{'}?\text{'}$ Finally, provide the solution of the CSP problem by running the query after $\text{'}?-\text{'}$

change$(50,x),$ labeling$([$ff$],x)$ in the box on the bottom right, and clicking "Run!".

Write the missing code and the solution for the variables below. $(5$ points$)$

DOMAINS $=$

CONSTRAINT $1=$

CONSTRAINT $2=$

CONSTRAINT $3=$

CONSTRAINT $4=$

CONSTRAINT $5=$

Solution: ONE$=$

$,$ TWO$=$

$,$ FIVE $=$

$,$ TEN$=$

Code Listing $1$: Money Exchange Problem