the currency of strange country has coins worth cents and cents write program to determine the largest purchase price that cannot be paid using these two coins here is an old puzzle you can solve using brute force by using computer program to check all the possibilitiesin the calculation every digit is precisely one away from its true value what is the correct calculation write program that finds all integer solutions to pell' equation where and are between and write program that asks the user for number and prints out all the ways to write the number as difference of two perfect squaresx where and are both between and writing number as difference of two squares leads to clever techniques for factoring large numbers write program that simulates all possible rolls of four dice and for each simulated rollfinds the sums of pairs of dice for instanceif the roll is the sums are , and for each of the possible sums from to find the total number of simulated rolls in which the sum appears and what percentage of the simulated rolls had those sums appear output the totals and percentagesnicely formattedwith the percentages formatted to one decimal place to check your workyou should find that the sum comes up in rollswhich is of the rolls in magic squareeach roweach columnand both diagonals add up to the same number partially filled magic square is shown below write program to check through all the possibilities to fill in the magic square the following is useful as part of program to play minesweeper suppose you have list that consists of zeros and ' write program that creates new list that has ' in the same placebut the zeroes are replaced by counts of how many ' are in adjacent cells (adjacent either horizontallyverticallyor diagonallyan example is shown below [hintshort-circuiting may be helpful for avoiding index-out-of-range errors pascal' triangle is shown below on the outside are ' and each other number is the sum of the two numbers directly above it write program to generate pascal' triangle allow the user to specify the number of rows be sure that it is nicely formattedlike below