Problem 2 (Birthday Problem)

Starting on their fourth birthdays a brother and sister each receive books on their birthdays, always getting as many books as their age. How old will the two siblings be when they have received a total of 100 books between them over their lifetimes ?

Solution

We make a table showing the total number of books each sibling accumulates as a function of age.

Age	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Books	0	0	0	4	9	15	22	30	39	49	60	72	85	99	100+

Since the total number of books accumulated by both siblings is the sum of two numbers in the second row of the table, we see that the only two numbers which sum to 100 are 15 and 85, which implies the siblings are 6 and 13 years old.

[Previous]	Problem 1 (Aztec Problem)
[Next]	Problem 3 (Friday-the-13th Problem)
[Up]	November Solutions
[Home]	Home Page
[Mail]	Send EMail to Maine Math Talent Search
[Contents]	Maine Math Talent Search Contents

Last modified on Tuesday, January 12, 1999