Problem 6 - solution

Solution to Problem 6

Let a and b denote the numbers in two of the squares as shown in the figure below, and compute the two neighboring entries in terms of them.

$\begin{picture}(250,250) \put(0,0){\line(0,1){250}} \put(0,0){\line(1,0){250}} \... ...170,220){{\bf *}} \put(215,120){{\bf 186}} \put(115,70){{\bf 103}} \end{picture}$

Then the common difference in the third row in the third row is b-2a, while in the fourth row it is 2b-a-74. Consequently

$\begin{displaymath}2a+4(b-2a)=186\quad\mbox{ and }\quad a+2(2b-a-74)=103.\end{displaymath}$

Solving these equations simultaneously, we find that a=13 and b=66. Therefore, the entries in the third and fourth rows, and then in the fourth column may be computed to find that the number in the square marked by the (*) is 142. For completeness, the figure below shows the rest of the entries as well.

$\begin{picture}(250,250) \put(0,0){\line(0,1){250}} \put(0,0){\line(1,0){250}} \... ...,120){{\bf 186}} \put(215,170){{\bf 179}} \put(215,220){{\bf 172}} \end{picture}$

Questions and/or comments should be directed to Judy Downey or Griff Elder

BACK

Last modified: Mon Oct 9 09:09:12 CDT 2000