by Aziz Inan |

Saturday, 19 December 2015 next month will mark world-wide known French cabaret singer, songwriter and actress Édith Piaf’s centennial birthday [1]. In Piaf’s memory and to celebrate her 100^{th} birthday, I constructed the following numerical brainteasers:

If numbers 1 to 26 are assigned to the letters of the French alphabet as A being 1, B is 2, C equals 3, etc., the numbers assigned to the letters of “Édith” and “Piaf” each add up to 46 and 32 respectively and note that the reverse of 46 (64) is double 32.

The prime factors of Piaf’s new age 100 are 2 and 5 where 2^{5} equals 32, representing “Piaf”. In addition, primes 5 and 2 put side by side make 52 and note that this year marks the 52^{nd} anniversary of Piaf’s death (she died on 10 October 1963). Also, 100 equals 10 x 10 where 10 and 10 side by side as 10-10 represents 10 October, the day Piaf died 52 years ago. Also, note that the sum of the digits of 46 (“Édith”) equals 10 (the day and the month number when Piaf died) and the sum oftheir squares is 52 where the reverse of 52, namely 25, equals the sum of the prime factors of 46.

If Piaf’s birthday 19-12-1915 is split into two four-digit numbers consisting of its odd- and even-numbered digits as 1111 and 9295, the sum of the digits of these two numbers are 4 and 25 each where 4 times 25 yields Piaf’s new age 100.

Piaf died on the 283^{rd} day of 1963, where the reverse of 283, which is 382, equals the product of primes 191 and 2. Interestingly enough, 191 and 2 put side by side make 1912, representing Piaf’s birth date, 19 December.

The sum of the squares of the digits of 1912 (Piaf’s birth date 19 December) equals 87, with reverse 78, which equals 46 “Édith” plus 32 “Piaf”. Also, 87 equals 3 times 29 where 3 plus 29 is 32 (“Piaf”) and reverse of 29, which is 92, equals twice 46 (“Édith”).

Piaf’s 100^{th} birthday is to occur on 19-12-2015. Interestingly enough, the leftmost and the rightmost halves of this date (1912 and 2015) have a hidden relationship. How so? First, split 1912 into its odd- and even-numbered digits as 11 and 92, and put these side by side to obtain 1192. Next, add the reverses of 1912 (2191) and 1192 (2911), and reverse the result. What comes out? (Answer: 2015.)

The prime factors of 1912 (which are 2 and 239) add up to 241, the reverse of which is 142. If 1915 (Piaf’s birth year) is split in the middle into 19 and 15, the reverses of these two numbers also add up to 142. Also, note that 142 equals twice 71 and interestingly enough, Piaf was born on the 353^{rd} day of 1915 where 353 is the 71^{st} prime number.

Interestingly enough, the numbers assigned to Piaf’s birth name “Édith Giovanna Gassion” add up to 3 times 71. Also, the reverse of the sum of primes 3 and 71 yield 47, the age Piaf died.

If 1912 is split in the middle as 19 and 12, the reverses of these two numbers differ by 70, which equal the number of days between Piaf’s death and her 48^{th} birthday.

If 1915 is split as 191 and 5, twice one more than the product of these two numbers yield 1912.

Piaf’s 125^{th} birthday to occur in 2040 will also be special since the numbers assigned to the letters of her world-famous song “La Vie en rose” add up to 125. Also, interestingly enough, if 10-10-1963 (the day Piaf died) is split into 10, 10, 19, and 63, 10 plus 10 gives 20 and 10 + 10 + 19 + 63 = 102, and 20 times 102 equals 2040, the year of Piaf’s 125^{th} birthday.

Piaf’s 201^{st} birthday to occur in 2116 will also be unique since first, 2116 equals the square of 46 (“Édith”), second, the reverse of the difference of the prime factors of 201 (3 and 67) is 46 (“Piaf”), third, the reverse of 201, which is 102, equals 10 + 10 + 19 + 63 (which make up 10-10-1963), and fourth, the reverse of twice the sum of 21 and 16 (which side by side is 2116) yields 47, the age Piaf died.

Happy 100^{th} birthday, Édith Piaf!

Aziz Inan is an Electrical Engineering professor at the University of Portland. He can be reached at ainan@up.edu.

[1] Édith Piaf, Wikipedia

https://en.wikipedia.org/wiki/%C3%89dith_Piaf