Farewell Birthday Brain Teaser for Provost Emeritus Tom Greene

University of Portland provost emeritus Tom Greene officially retired on June 30, and as a token of his esteem, Aziz Inan, Shiley School of Engineering, put together the following farewell birthday trivia brain teaser to thank him for his leadership and friendship:

1. Multiply the left and right halves of Tom’s birth year Y₁Y₂Y₃Y₄ to obtain the number X. Then, look up the X^th prime number. Next, subtract the X^th prime number from the reverse of Tom’s birth year, namely Y₄Y₃Y₂Y₁ and read the result backwards. Surprise!
2. Further, if Tom’s full birthday M₁M₂/D₁D₂/ Y₁Y₂Y₃Y₄ is split into M₁M₂, D₁D₂, Y₁Y₂, and Y₃Y₄, interestingly, half of the sum of M₁M₂ and D₁D₂ yields Y₁Y₂, and twice the difference of M₁M₂ and D₁D₂ results in Y₃Y₄.
3. Tom’s birthday this year (2020) is numerically special: double the sum of the squares of the month and day numbers of his birthday. What comes out?
4. The reverse of the difference of the squares of the digits of Tom’s new age this year equals the sum of the letter numbers of his last name, Greene.
5. Tom’s 75^th birthday will be special since the reverse of 75, namely 57, equals the sum of the letter numbers of his middle name, George.
6. Tom’s 76^th birthday will also be special since 76 equals the sum of the letter numbers of Thomas. Additionally, the rightmost two digits of that year equals the difference of the month and day numbers of his birthday.
7. Tom’s 83^rd birthday will be special too since 83 equals the sum of the reverses of the month and day numbers of his birthday, namely (M₂M₁ + D₂D₁).
8. Tom’s 89^th birthday will be a five-digit palindrome date. Also, 89 is the 24^th prime number (see item # 6).
9. His 90^th birthday will be special too since Y₃Y₄ = M₁M₂ + D₁D₂.
10. Tom’s 100^th birthday expressed as M₁M₂/D₁D₂/ Y₁Y₂Y₃Y₄ has a special property: Y₁Y₂Y₃Y₄ = 2^{(M1+M2+D1+D2)}.
11. Tom’s 153^rd birthday in the year Y₁Y₂Y₃Y₄ will also be special: Y₁Y₂Y₃Y₄ = M₁M₂D₁D₂ + D₂D₁M₂M₁. Moreover, count the number of days left in the year after Tom’s birthday.
12. Tom’s 189^th birthday will be a seven-digit palindrome date.
13. Lastly, Tom’s 508^th birthday contains every whole number from 0 to 7, each appearing once.

For more information or to commission your own brain teaser, contact Inan at ainan@up.edu.