Question 30
Consider a 15 × 15 grid of unit squares. In the square in row a and column b, we write the number a × b. We then colour the squares black and white in a checkerboard fashion, so that the square labelled 225 is coloured white. The diagram shows the parts of the grid near each corner. What are the last three digits of the sum of the numbers in the white squares?
Editable corner table: W = white, B = black; omitted rows and columns follow the same rule.
|a \ b|1|2|3|…|14|15|
|---|---|---|---|---|---|---|
|1|1 W|2 B|3 W|…|14 B|15 W|
|2|2 B|4 W|6 B|…|28 W|30 B|
|3|3 W|6 B|9 W|…|42 B|45 W|
|…|…|…|…|…|…|…|
|14|14 B|28 W|42 B|…|196 W|210 B|
|15|15 W|30 B|45 W|…|210 B|225 W|
Editable corner table: W = white, B = black; omitted rows and columns follow the same rule.
|a \ b|1|2|3|…|14|15|
|---|---|---|---|---|---|---|
|1|1 W|2 B|3 W|…|14 B|15 W|
|2|2 B|4 W|6 B|…|28 W|30 B|
|3|3 W|6 B|9 W|…|42 B|45 W|
|…|…|…|…|…|…|…|
|14|14 B|28 W|42 B|…|196 W|210 B|
|15|15 W|30 B|45 W|…|210 B|225 W|