Puzzle of the day (06/26/09)
June 26, 2009
There is a snail climbing a 20-meter high pole. In a day, it climbs up 5m, but at night, it slips down 4m. How long does it take him to climb to the top?
Answer to last puzzle: 10
Explanation: [Easy/Unsure approach] Write down from 1 to 10 and simulate the paint job to see the pattern. You will see the post 1, 4, 9 turn back to red. All posts with squared number will be red and there are 10 of them. [Better approach] Each post will change color for each common divisor of its post’s number, i.e., post #8 has 4 divisors (1, 2, 4, 8 ) so it will be painted 4 times, post #9 has 3 divisors (1, 3, 9) so it will be painted 3 times. All squared numbers have odd numbers of divisor and there is only 10 squared numbers from 1 to 100.
Puzzle of the day (06/25/09)
June 25, 2009
Builderman has to built a fence to keep the enemies of of his base.
The fence has 100 black fence posts. Builderman goes through and paints each post red. Then he goes through again and paints every other post black. He goes through a third time and paints every third post. He paints the red posts black and the black posts red. He He does this a fourth time for every fourth post, then a fifth, then a sixth, until he has gone through 100 times total. He’s exhausted. How many posts are red?
Answer to last puzzle: 6
Explanation: Thinking of a filled 3-brick tall pyramid, we can build it by combining a hollow 3-brick tall one and one 1-brick tall one (2×2 brick). Then a filled 5-brick tall pyramid can be combined by a hollow 5-brick tall, a hollow 3-brick tall, and one 2×2 brick. Same idea and so on. To fill a 11-brick tall one, we can build it by combining a hollow 11-brick tall, 9-brick tall, … , 3-brick tall and 0ne 2×2 brick. So the total would be 6.
Puzzle of the day (06/24/09)
June 24, 2009
Builderman wants to build a strong pyramid, so he constructs a solid (completely filled) one. The rules are the same: using only 2×2 and 2×4 bricks, and must use 2×4 bricks when possible. How many 2×2 bricks must he use in a 11-brick tall pyramid?
Answer to last puzzle: 1
Explanation: Don’t be fool by the picture. Except the top level, every other level can be built by using 2×4 bricks.
Puzzle of the day (06/23/09)
June 23, 2009
Builderman is constructing a hollow pyramid out of 2×2 and 2×4 bricks.
Whenever he has the choice, Builderman opts to use a 2×4. How many 2x2s must Builderman use to create a pyramid that is 11 bricks tall?
