7. In the problems below the 1" digit in the binary expansion appears in the rightmost position while the 6 digit in the binary expansion appears in the leftmost position: a) Numbers from 1 to 63 are placed on 6 cards according to the following 7 rules: 1. The 1" digit in the binary expansion of each number on card 1 is a one. 2. The 2nd digit in the binary expansion of each number on card 2 is a one. 3. The 3 digit in the binary expansion of each number on card 3 is a one. 4. The 4th digit in the binary expansion of each number on card 4 is a one. 5. The 5 digit in the binary expansion of each number on card 5 is a one. 6. The 6th digit in the binary expansion of each number on card 6 is a one. 7. There are 32 numbers on each of the six cards. Professor Scarlett is looking at a number that appears on cards 2, 3, and 4 but not on cards 1, 5, and 6. What number are you looking at? Professor Scarlett is looking at: b) Numbers from 1 to 63 are placed on 6 cards according to the following 6 rules: 1. The 1" digit in the binary expansion of each number on card 1 is a one. 2. The 24 digit in the binary expansion of each number on card 2 is a one. 3. The 3 digit in the binary expansion of each number on card 3 is a one. 4. The 4" digit in the binary expansion of each number on card 4 is a one. 5. The 5 digit in the binary expansion of each number on card 5 is a one. 6. The 6 digit in the binary expansion of each number on card 6 is a one. Dr. Ecco found a twin prime that appears on cards 2, 3, and 4 but not on cards 1, 5, and 6. Even though the amount of numbers printed on each card is unknown it is still possible to find Dr. Ecco's number. What is his number? Definition: A prime number p is a twin prime if p + 2 or p - 2 is also a prime number. For example, 19 is a twin prime number since 17 is a prime number, while 23 is a prime number that is not twin since both 21 and 25 are not prime numbers. Dr. Ecco is looking at