You have a mobile with a keyboard which consists of 10 digits and two symbols, [#] and [*], as shown in the illustration.

On the mobile's screen is a small program which shows the same keyboard, but with the buttons in a different order. When you press a button on the keyboard, then the respective button on the same place on the screen is highlighted. That is: button [1] on the keyboard highlights button [6] on the screen; button [2] on the keyboard highlights button [7] on the screen; and so on. The object is to press consecutively some 5 buttons on the keyboard so that the same set of buttons is highlighted on the screen.

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There are 1000 soldiers. 70 lost an eye, 75 lost an ear, 80 lost an arm, and 85 lost a leg. At least how many lost all four? (Minimum number)

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There 3 floors of an apartment building with 12 residents. A storm comes that causes the ceiling of the top floor to leak. So the residents on the top floor go to the second floor to ask those residents for shelter, but they can only allow double their occupancy and the rest have to go back up to their floor. The water gets to the second floor and those residents go to the first floor to ask the same thing and they get the same reply (They can only take double their occupancy). The question is, how many residents were on each floor before the storm so that there are equal number of residents on each floor after the storm?

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There's a rabbit in a square surrounded by wolves. The wolves can only run along the edges of the square, the rabbit can move however it wants and it wants to get out of the square. The maximum speed of the wolves is 1.4 times the speed of the rabbit. How can the rabbit escape?

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In 1960, a man and his son went to Egypt to see the pyramids together for the first time. In 1979, the man went to see the pyramids in Egypt on his own for the very first time.

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D B J + A N D R E E + S E N D = C H E E R, You know that E^2 = H & the letters range from 0 to 9.

Find the number that corresponds to each letter (Assume carry over).

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Use three lines to create 9 non-overlapping triangles over “M”.

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Ants start at the vertex of a triangle. They begin walking along the lines of the triangle. What is the probability of collision? Assume: They walk the same speed, only go cw or ccw and each direction equally likely.

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Polish, beef, special sauce, onions, pickles, sauerkraut, banana peppers, jalapenos, mayo, celery salt, and relish. (11 items)

How many combinations of the items above could you get?

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A bunch of people are living on an island, when a visitor comes with a strange order: all blue eyed people must leave the island as soon as possible. There will be a flight out at 8:00pm every evening. Each person can see everyone else's eye color, but they do not know their own (not is anyone allowed to tell them.) Additionally, they do not know how many people have blue eyes, although they do know that at least one person does. How many days will it take the blue-eyed people to leave the island? Assume all people are intelligent.

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There are 5 photos in a family album, and 3 people in each photo. The person in the middle of the pictures is always different. The left person was always the middle man's son and the right person was always his brother. How many different combinations of people are there in all 5 photos?

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Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)?

An example that doesn't work: 7192/38456 = 0.187

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