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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

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[edited by: emassa at 1:54 PM (GMT -4) on 29 Mar 2023]
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Parents
• 1. n(n+1)/2=946 --> n=43 (sum of first consecutive integers)

2. If m is the age of Ann, the age of Helen is m-5. So m(m+1)/2 + (m-5)(m-4)/2 = 1687. By solving the equation you get m= 43, so Anne is 43 and Helen is 38.

• You can also calculate this easily in Excel. Just make a column (column A) with numbers 1,2,3, etc. In the column next to it calculate the number of candles. The first cell (B1) gets: SUM(\$A\$1:A1) and drag this down. You will see that at age 43 946 candles have been blown out. Now copy both columns with an offset of 5 downwards and you will get the results for a second person 5 years younger. Now make a new column with the sum of the candles of each sister and you will get the total number of candles blown out by both sisters. You will easily find that for 1687 sister 1 is 43 and sister 2 is 38.

Reply
• You can also calculate this easily in Excel. Just make a column (column A) with numbers 1,2,3, etc. In the column next to it calculate the number of candles. The first cell (B1) gets: SUM(\$A\$1:A1) and drag this down. You will see that at age 43 946 candles have been blown out. Now copy both columns with an offset of 5 downwards and you will get the results for a second person 5 years younger. Now make a new column with the sum of the candles of each sister and you will get the total number of candles blown out by both sisters. You will easily find that for 1687 sister 1 is 43 and sister 2 is 38.

Children
• Yeah Fons,

Any tools, methods including crystal ball are accepted! what counts is the final result! Here also, your answers will be conformed next week!