# The Paintings Puzzle

An art gallery features a modern work of ‘moving art’. The artist stands by a stack of paintings, each featuring a different number. One of the paintings is displayed on the wall. At certain times the artist removes the painting from the wall and replaces it with a painting from the stack. At 11am, the artist hangs a painting of the number 30. At 4pm he hangs a painting of number 240. At 7.30pm he hangs a painting of number 315. What painting does the artist hang at 9.20pm?

The answer is 200. The explanation is that the painting number equates to the number of degrees between a clock’s hour-hand and minute-hand (measured in a clockwise direction). The first three examples are easy if you sketch the clock hands on a clock face and plot the hours around the clock face (bear in mind there are 360 degrees around a circle; the 12 on the clock-face equates to 360 (or zero) degrees, and each hour equates to 30 degrees, being one-twelfth of 360). The puzzle question (9.20pm) is more difficult to calculate than the first three time examples. Here are my two attempts to explain it:

method 1- Each hour on the clock face equates to 30 degrees (12 x 30 = 360). From 9 to 4 on the clockface moving clockwise is 210 degrees (7 hours x 30 degrees = 210 degrees). But the hour hand is not on the 9, it’s one-third of the way to 10 (the time being 9.20, not 9.00). This one-third (being 20 minutes of a 60 minute hour) equates to 10 degrees (10 is a third of 30 degrees). Therefore the angle in degrees between the hour hand and the minute hand at 9.20 is 200 degrees (210 – 10).

method 2 – At 9:20 the minute hand is at the number 4 which is 120 degrees from zero (4 is a third of 12, hence a third of 360 degrees is 120 degrees). The hour hand is at a position equating to 560/720 minutes (there being 720 minutes in 12 hours, and 9hrs 20mins being 560 minutes). 560/720 equates to 280/360 (360 is half of 720, and half of 560 is 280), so the hour hand is at 280 degrees from zero (remember zero is 12 on the clock face). Measured in a clockwise direction, the number of degrees (or angle) between the hour hand and the minute hand is 80 degrees around to to the 12 (at zero degrees), plus 120 degrees from the 12 to the 4 (which we previously established). Then simply add: 80 + 120 = 200.

### Your Answer

## More puzzles to try-

### How did he know to stop?

A man was driving a black car. His lights were off. The moon shown no light. A cat was in ...Read More »### Make a word

Form a word from the letters and hyphen mark below: A B C D E F G I –Read More »### How many cards does each man have and how many cards do they trade?

Joe deals himself and his friend John some cards from a deck of cards (not the same amount). If John ...Read More »### Solve the murder mystery

A homicide team enters a crime scene where a dead body of a fat old man lies there on the ...Read More »### Divide barrels and wine evenly

A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven ...Read More »### Find the odd

Which of the below owl is odd one out?Read More »### Bulbs in circle puzzle

On a circle there are 2014 light bulbs, 2 are ON, and 2012 are OFF. You can choose any bulb ...Read More »### What are their ages in years?

The grandson is about as many days old as the son is in weeks. The grandson is approximately as many ...Read More »### No flesh and nor feather

They have not flesh, nor feathers, nor scales, nor bone. Yet they have fingers and thumbs of their own. What ...Read More »### Can you find out those identical cats?

The nine cats below are not identical Only two of them are identical. Can you find out those two identical ...Read More »### Runs without legs

What runs without legs ?Read More »### Doll but not for play

It is like a doll, But not for playing; It stand up straight, but if windy it may be laying; ...Read More »### Sticks and time measurement riddle

There are two sticks. Each stick takes one hour to burn. These sticks are not identical, nor are they uniform. ...Read More »### Santa mistake on Christmas puzzle

Santa distributes 2 gifts to every child in the street at the Christmas evening. He mistakenly gives 4 gifts to ...Read More »### Same father for women and daughter puzzle

A women and her daughter walked into a restaurant. A man walked past and the women both said, “Hello, Father”. ...Read More »### What is the next two rows of numbers?

The below is a number puzzle. It should be read left to right, top to bottom. 1 1 1 2 ...Read More »### Modern Scholars puzzle

Many years ago, befor modern educashun in the new millenium, one problem in skools was baseic speeling and grammer. To ...Read More »### He is always to be riddle

He never were, is always to be. No one ever saw him, nor ever will. And yet he is the ...Read More »### Poor and King

The cost of making only the maker knows, Valueless if bought, but sometimes traded. A poor man may give one ...Read More »### New York Traffic Laws puzzle

A bus driver was heading down a street in New York. He went right past a stop sign without stopping, ...Read More »