Tests have 3 x 3 matrix and there is some logic sequence, which you have to figure out and choose the missing piece from six samples that are given to you.

Do you have any idea?

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January: 7110

February: 826

March: 5313

April: 541

May: 3513

June: 4610

July: 4710

What is the code for the month of August?

Abraham finds that the fuselage and fuel system of returned planes are much more likely to be damaged by bullets or flak than the engines. What should he recommend to his superiors?

]]>If he keeps at it, what are his expected winnings?

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Now instead lets divide each square diagonally from the top left corner to the bottom right corner. What is the fewest amount of yellow colorings needed?

]]>The traditional dimensions of the board is 7 wide by 6 tall.

For which dimensions does the first player have a winning strategy?

]]>The traditional dimensions of the board is 7 wide by 6 tall.

For which dimensions does the first player have a winning strategy?

]]>You have a bag of gold coins. They are all of the exact same weight except one, which is a fake.

You have a balance scale, which you can only use N times. What is the maximum number of coins from which you can pick out the fake?

]]>The HR system is a piece of software that automatically creates mathematical concepts and discovers conjectures about them. The system is now capable of generating and testing the solvability of puzzles within wide constraints, and we’ve developed a set of puzzles we’re calling Donatsu (transliterated Japanese for “Doughnut”). These involve the player following a loop (or various other loop-like designs) attempting to get a series of numbers to reach particular totals through adding mathematical operators (+, -, /, and x).

I've pasted in below four of the many permutations we've developed - Uninatsu (the most basic), Chromanatsu, Maxinatsu, and Hexanatsu (the most complex) - alongside appropriate instructions. You can also download to print off a paper version, since these are paper puzzles, after all! Our long-term goal is to develop and refine these to the point that we can potentially get some published in newspapers.

Seeing as these are designed to be done with pen and paper, you can download a PDF of all the puzzles here: http://www.ultimaratioregum.co.uk/game/download/donatsu-v1/?wpdmdl=6391

So: we'd love to get your feedback! Aside from the obvious - are these fun and interesting to solve - we'd also like to ask two main questions: 1) which did you like most, and why, and 2) what would you improve about the puzzles? This is still the early stage of development, so we're trying to pin down the best puzzle permutations possible. Thanks!

The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs.

By finding the first arrangement to contain over 10^{12} = 1,000,000,000,000 discs in total, determine the number of blue discs that the box would contain.

Two people wish to cross a river. There is only one boat. The boat can only carry one person at a time. A person can not cross the river unless in the boat. The boat can not cross the river without someone in it. Both people cross the river. Can you explain how it happened?

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