Puzzle of the week

How can you construct a plane where every point is coloured either black or white such that two points of the same colour are never a unit distance apart?


Previous puzzle

Alex and Bob work as financial advisors for the same company. They draw equal salaries from the company. They behave well at the office. Both work on similar assignments. Each assignment requires a yes-no decision. The company uses the decisions made by them to make profits.

After the recession hit the company very badly, one of them has to be fired. Both Alex and Bob have worked on almost the same number of assignments in the last ten years. Alex has been consistently taking about 80% decisions correctly every year. Bob, on the other hand, has been taking only about 5% correct decisions every year.

Assuming that the performances of Alex and Bob would remain the same in future, who should the company fire to maximize its profits in the years to come? Why?


Random puzzle from the past

About 50 people were invited to a potluck. Each invitee was required to bring an equal number of homemade cookies to the potluck.

In the potluck, 1287 cookies brought by the guests were poured into the pot and shuffled. The cookies were then distributed equally among all the guests present. No cookies were broken.

Sam was one of those who completely forgot about bringing cookies to the potluck. About 20 people with cookies had arrived at the potluck before him. How many cookies did Sam get?


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