Contest [Issue 33] Test Your Intellect!

[Pathfinder 1,690]

The English Newspaper is well known for organising contests that test your writing skills, so I thought I would organise something that may appeal to the more mathematically minded out there.

Below are three Tanki related problems, in no particular order of difficulty. Prizes of 15,000, 10,000 and 5,000 crystals are given to the fastest three who complete each of the three problems. So, get them all right first and win yourself a hefty 45,000 crystals for a few simple sums!

You may submit your answers in the form below - you can submit your answers one at a time, but for each question you do, only your first entry will be accepted.

http://goo.gl/forms/XQfiC8CKYa

Good luck!

Edited July 30, 2017 by Hexed

[Pathfinder 1,690]

Question 1:

 

Which square in the grid minimises the average distance to the gold drop zones in the map Noise? To describe the square, give me the column number, followed by the row number. Since the gold zones sometimes span multiple squares, assume the gold is in the square that has the largest share ofthe gold zone. To further reduce ambiguity over which square the gold lies in, I will be accepting a range of squares for the final answer.

 

Credit to for the picture.

 

Edited March 22, 2015 by Pathfinder

[Pathfinder 1,690]

Question 2:

 

At a particular point in time, time = 0, a fully micro-upgraded Hornet M3, travelling at top speed, leaves the north gate and travels down the map, depicted by the light blue arrow. At the same time, a fully micro-upgraded Dictator M3, travelling at top speed, leaves the south gate and travels up the map, depicted by the green arrow. Both tanks continue at top speed, and do not decelerate.

 

At some time, time = t, a fully micro-upgraded M3 Railgun user can fire one single railgun shot to hit both the Hornet and Dictator, with the Railgun pointing across the map (perpendicular to the movement of the Hornet and Dictator).

 

Given that the distance between the north and south gates is 120 metres, find the vertical distance of the Railgun from the North gate, and find the time, t, at which the Railgun user must fire.

 

Credit to @DarthvaderjonGTR for the picture.

Edited March 27, 2015 by Pathfinder

[Pathfinder 1,690]

Question 3:

 

The diagram shows the major paths as arcs which can be used to travel between the flags in Sandbox. How many different ways are there for travelling between both flags, without returning to any point previously visited?

 

Extension: What about if the question was to find the number of routes between the flags if you can visit the same point multiple times, but you can't use the same arc more than once?

 

Credit to @DarthvaderjonGTR for the picture.

 

Edited March 22, 2015 by Pathfinder