shortest path riddle
A 12 by 25 by 36 inch box is lying on the floor on one of its 25 by 36 inch faces. An ant, located at one of the bottom corners of the box, must crawl along the outside of the box to reach the opposite bottom corner. It can walk on any of the box faces except for the bottom face, which is in flush contact with the floor. What is the length of the shortest such path?
One obvious route is for the ant to crawl along the line of contact between the box and the floor.
This is clearly 25 + 36 = 61 cm in length.
Can the ant find a shorter path by crawling over the top of the box?
The key insight is to flatten the box. Having done this, it’s clear that the shortest path must be one of the straight line paths from one corner to its opposite. There are four such paths. They are the diagonals of:
- a 36 by 12+25+12 cm rectangle
- a 25 by 12+36+12 cm rectangle
- two 12+25 by 12+36 cm rectangles
Using Pythagoras’ Theorem, the lengths of these diagonals are, respectively, the square roots of 3697, 4225, and 3673. Note that 612 = 3721, and so the path along the line of contact between the box and the floor is longer than all but one of these diagonals.
The shortest path over the box is therefore cm, or a little over 60.6 cm.
More puzzles to try-
- 3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
- Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
- There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
- Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »
- Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
- In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »
- Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with ...Read More »
- A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »
- In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »
- A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
- There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »
- Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
- Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
- A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
- In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »
- Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
- A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
- Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »
- Which letter replaces the question markRead More »
- A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »