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# KCC's Quizzes AQQ231 about Birthdays and Cake Candles

Mary celebrates her birthday every year from the very first year.

The number of candles on her cake used reflects her age : 1 at age of 1, 2 at age of 2, 3 at age of 3 etc…

Up to now, she has blow out a total of 946 candles.

Questions:

1. How old is Mary today?
2. In an other family, there are 2 sisters, Ann and Helen. Helen is 5 years younger than Ann. They both follows the same scenario for the candles as Mary. The cumulated candled used by the 2 sisters is 1687. How old are Ann and Helen?

P.S. If you think there are still colleagues or friends (internal or external) you think who can be interested in those quizzes, please let let them know....

Kuo-Chang

Hide replies until user replies.
[edited by: emassa at 1:54 PM (GMT -4) on 29 Mar 2023]
• Thank you Sona for your feedback! Rendez-vous next week!

• Guten Tag Roland! Yes, as already said to Fons: any method is valid as long as the answer is correct!

1. Mary is 43yrs

2. Helen is 38yr,s Ann 43yrs

• OK, let's publish now the official answers...

1. The total number of candles used by Mary is thus : S=1+2+3+4…+n where n is the today age. S = n(n+1)/2 = 946, or n² + n = 1892 or n² + n -1892=0

n = [-1 +/-SQRT(1+4*1892)]/2 = 43 years old

1. Ann has consumed n(n+1)/2 candles in total and Helen m(m+1)/2. Since Helen is 5 years younger, we have m=n-5, both sisters have used:

n(n+1)/2 + m(m+1)/2 = n(n+1)/2 + (n-5) (n-4)/2 = n² - 4n +10 = 1687

Hence : n² - 4n - 1677 = 0 or n = [4 +/-SQRT(16+4*1677)]/2

n = 43 this the Ann’s age

m=n-5 = 38 is the Helen’s age

There are also solutions using Excel spreadsheet that was opted by many

Big applause for our 4 first winners:

1. Jeff EVANKO, ADI, Key Account Manager, Cleveland (OH, USA

2. John WISNIEWSKI, ADI, Snr Field Application Engineer, Flourtown (PA), USA

3. Rahul NOOLU, ADI, Design Verification Manager, Bengaluru, India

4. Gaetano PIARINO, ADI, Key Account Manager, Milan, Italy