Consider a number system in which the k-th digit can have values 0, ..., k; so the rightmost digit is 0 or 1, the next 0, 1, or 2, the next 0, 1, 2, or 3 etc. Counting in this system from one to twenty is 1, 10, 11, 20, 21, 100, 101, 110, 111, 120, 121, 200 201, 210, 211, 220, 221, 300, 301, 310. The largest numbers that can be expressed with one to four digits are 1 (value 1), 21 (value 5), 321 (value 23), 4321 (value 119) Show that the value of the k-digit number represented by 100 0 (with k 1 zeros) is k!. Consider a number system in which the k-th digit can have values 0, ..., k; so the rightmost digit is 0 or 1, the next 0, 1, or 2, the next 0, 1, 2, or 3 etc. Counting in this system from one to twenty is 1, 10, 11, 20, 21, 100, 101, 110, 111, 120, 121, 200 201, 210, 211, 220, 221, 300, 301, 310. The largest numbers that can be expressed with one to four digits are 1 (value 1), 21 (value 5), 321 (value 23), 4321 (value 119) Show that the value of the k-digit number represented by 100 0 (with k 1 zeros) is k