IBM Research | Ponder This | April 2001 solutions

# Ponder This

## April 2001

<<March April May>>

\$618,042.45.

Any college on the planet.

Each penny deposited to the son's account in the first month eventually causes a total of \$1,964.17 in his account and \$3,178.11 in the daughter's account.

Each penny deposited to the daughter's account in the first month eventually causes a total of \$1,964.17 in her account and \$1,213.94 in the son's account.

If the initial deposits are x cents and y cents, the daughter's wealth tells us that

3178.11x + 1964.17y + 7.50 = 1000000.00,
whose only solution (in positive integers) is x=73, y=391.

The son's wealth is then
1213.94*391 + 1964.17*73 + 7.50 = 618,042.45.

The monthly deposits are

3.91, 0.73, 4.64, 5.37, 10.01, 15.38, 25.39, 40.77, 66.16, 106.93, 173.09, 280.02, 453.11, 733.13, 1186.24, 1919.37, 3105.61, 5024.98, 8130.59, 13155.57, 21286.16, 34441.73, 55727.89, 90169.62, 145897.51, 236067.13, 381964.64, 618031.77.

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