Insight 10 - Puzzle Prime

Batting Averages

Section: Brain Teasers Category: Insight

Difficulty: Advanced

David Justice and Derek Jeter were professional baseball players. In 1997 they had the following conversation:

David: Did you know that in both 1995 and 1996 I had better batting averages than you?

Derek: No way, my batting average over the last two years was definitely higher than yours!

It turned out that both of them were right. How is it possible?

SOLUTION

This is the so called Simpson’s paradox. The reason it occurred is that during 1996 both players had high averages and Derek Jeter had many more hits than David Justice. In 1996 both players had low averages and David Justice had many more hits than Derek Jeter. You can see their official statistics below.

Player	1995	1996	1995-1996
Derek Jeter	12/48 (.250)	183/582 (.314)	195/630 (.310)
David Justice	104/411 (.253)	45/140 (.321)	149/551 (.270)

Unknown Author November 24, 2020

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String of Words

Section: Brain Teasers Category: Insight

Difficulty: Expert

There is a common 9-letter word in the English language, such that if you keep removing its letters one by one, the resulting 8 words are still valid. What is this word?

Remark: The removed letters do not need to be from the beginning or the end of the word.

SOLUTION

The word is STARTLING -> STARTING -> STARING -> STRING -> STING -> SING -> SIN -> IN -> I.

Unknown Author November 12, 2020

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Ancient Invention

Section: Brain Teasers Category: Insight

Difficulty: Easy

There is an ancient invention still used today in some parts of the world which allows people to see through walls. What is it?

SOLUTION

The answer is WINDOWS.

Unknown Author November 9, 2020

1 Comment

Thief

Section: Brain Teasers Category: Insight

Difficulty: Easy

A woman was standing in her hotel room, when somebody knocked on the door. When she opened the door, there was a man who said that he has mistaken his door, apologized, and continued down the corridor. When the woman closed the door, she called security to warn them about the thief. Why did she think the man was planning to rob her?

SOLUTION

If the man really thought this was his room, he wouldn’t have knocked on the door.

Unknown Author October 15, 2020

2 Comments

Crowns and Lions

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Split the grid into four identical regions, such that each region contains a lion and a crown.

SOLUTION

The solution is shown below.

Henry Dudeney September 24, 2020

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5 Lines With 4 Points

Section: Brain Teasers Category: Insight

Difficulty: Medium

On the image below you can see 11 points in the plane placed in such a way that there exist 6 lines passing through 4 points each. Can you place 10 points in the plane, such that there are 5 lines passing through 4 points each?

SOLUTION

Simply draw a pentagon.

Unknown Author August 24, 2020

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Old Man’s Killer

Section: Brain Teasers Category: Insight

Difficulty: Medium

An eighty-year-old person was living alone in his house. On a sunny Friday morning, while delivering some letters in the mailbox, the postman felt suspicious and decided to look through the window of the house. That’s when he saw the old man lying dead on the floor in a puddle of blood. When the police arrived, they found three bottles of milk, the Tuesday’s newspaper, and some gifts in front of the house. The lock of the door was broken, and they already suspected a person. Whom and why?

SOLUTION

The police suspected the newspaper boy. Since there were 3 bottles of milk, the old man must have been dead for a few days already. However, the last newspaper left in front of his house is from Tuesday. Probably the newspaper boy, knowing that the old man is dead, decided that there is no point to go to his door and deliver newspapers anymore.

Unknown Author August 15, 2020

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Puzzil Primus

Section: Brain Teasers Category: Insight

Difficulty: Medium

Puzzil Primus was born on the 314th day of year 20B.C. and died on the 271st day of year 20A.D. How old was he when he died?

SOLUTION

Puzzil Primus was 38 years old. This is because day 314 comes after day 271, and also there is no year 0 in the calendar.

Unknown Author August 3, 2020

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Knights and Coins

Section: Brain Teasers Category: Insight

Difficulty: Hard

Bob and Jane are taking turns, placing knights and coins respectively on a chessboard. If Bob is allowed to place a knight only on an empty square which is not attacked by another knight, how many pieces at most can he place before running out of moves? Assume that Jane starts second and plays optimally, trying to prevent Bob from placing knights on the board.

SOLUTION

Bob can place at most 16 knights. One way to do this is to keep placing knights only on the 32 white squares. In order to see that Jane can prevent Bob from placing more than 16 knights, split the board in four 4×4 grids. Then, group the squares in each grid in pairs, as shown on the image below. If Bob places a knight on any square, then Jane will place a coin on its paired square. This way Bob can place at most one knight on each of the four red squares, one knight on each of the four green squares, one knight on each of the four brown squares, and one knight on each of the four blue squares. Therefore, he can not place more than 64/4 = 16 knights on the board.

Unknown Author July 27, 2020

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Light Bulbs in the Attic

Section: Brain Teasers Category: Insight

Difficulty: Hard

There are three light bulbs in your attic. All of them are turned off and their switches are installed downstairs. You can play with the switches as much as you want and after that, you can visit the attic above just once. How can you find out which switch to which bulb corresponds?

SOLUTION

You turn the first switch on, then wait for 30 minutes and turn the second switch on. After that go upstairs and examine the bulbs. The one which is turned off corresponds to the third switch. The one which is turned on and is still cold corresponds to the second switch. The one which is turned on and is hot corresponds to the first switch.

Unknown Author July 21, 2020

2 Comments