Problematics: Godzilla does geometry

In this week's Problematics, we bring together movie giants Godzilla, King Kong and, a creation of internet, giant squid.

Written by Kabir Firaque | New Delhi | Updated: April 15, 2015 1:53 pm
Godzilla-Japan-759 Godzilla vs King Kong vs Giant Squid.

Why Godzilla? Because he has just been paid a tribute while poor King Kong has missed out. They deserve a joint tribute, these two monsters with a shared movie history, which is why they have come together to “Problematics” this week.

Godzilla is a Japanese creation borrowed by Hollywood. Last week, Japan mounted his head at a height of 52 m in Tokyo. But we need all of Godzilla, not just his head, so count 52 m as his full height.

King Kong is a Hollywood concept borrowed by the Japanese, most notably in King Kong vs Godzilla (1962). Varying in height from movie to movie, he was 20 m tall in King Kong Escapes (1967), which is just the height we’re looking at. Add to cart.

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Finally, there is a giant squid whose pictures went viral in 2014 after it was supposedly washed up on a California beach. He turned out to be a hoax, which doesn’t matter. It’s size that does matter, Godzilla insists, and we find that the alleged size of the alleged squid was 48 m. Add to cart and proceed to checkout.

Godzilla-alignment Godzilla vs King Kong vs Giant Squid.

They align themselves as shown in the visual representation above by my colleague Sanjay Tambe. Squid stretches out between Kong and Godzilla’s feet, while Godzilla leans forward until his head touches Kong’s. They fit together neatly, much to the delight of Pythagoras.

(Kong × Kong) + (Squid × Squid) = (Godzilla × Godzilla)
=> (20 × 20) + (48 × 48) = (52 × 52)
=> 400 + 2,304 = 2,704

These are large numbers, though, and need to be scaled down. Let 4 metres = 1 Problematic unit. Then, Kong measures 5 Problematics, Squid 12 Problematics, and Godzilla 13 Problematics. That’s much better.

They still obey Pythagoras; (5×5) + (12×12) = (13×13). Additionally, they go off on their own trip.

Perimeter of their alignment
= Kong + Squid + Godzilla
= 5 + 12 + 13
= 30 Problematics

Also, area of the alignment
= ½ × Kong × Squid
= ½ × 5 × 12
= 30 square Problematics

This is something very rare, a matching perimeter and area. Among all right-angled triangles whose sides are in whole numbers, only two enjoy such a match. One of these rare triangles is the one above, with sides of 5, 12 and 13 units.

Puzzle#6A: Find the dimensions of the other such triangle.

What you wrote

Of the two puzzles last week, Puzzle#5B had a mistake initially. The original version asked for an anagram of AREA CULPRIT but it didn’t translate into PARTICULATE, as M Natrajan pointed out. Thanks to his alert, I could change it to ATE A CULPRIT before it was too late. Sorry about the mistake.

The answer to Puzzle#5B is PARTICULATE. Pretty much a killer it is!
Lakshmi Swathi Gandham
***
ATE A CULPRIT = PARTICULATE.
Anil Kumar, Sampath Kumar V, Shalesh Kumar (separate letters)
***
Mr Kabir — Puzzle#5A solved by my cousin Janani N P (10th Standard, St. Joseph’s School, Coimbatore) with a bit of help from my side.
Number of guys who have travelled to all three regions = 1.2
Number of guys who have permanently settled down in North = 1.8
Number of guys who have permanently settled down in South = 2.4
Number of guys who have permanently settled down in East = 3.0
Sampath Kumar V (IIM-K alumnus)
***
Kabir — Find attached image for Puzzle#5A. Thought a Venn diagram would do better justice than me writing down the answers.
M Natrajan, IIM-C (Class of 2009)

Natrajan’s Venn diagram.

 

Please tender exact change

Puzzle#6B: Take all rupee denominations currently in circulation, coins as well as notes. Ignore paise, though. Now manage your change.
(i) If you have exactly one currency unit of each denomination from Re 1 to Rs 50, which amounts below Rs 100 will you never be able to put together?
(ii) If you are allowed as many coins and notes as you want between Re 1 and Rs 50, what is the smallest amount you will need to assemble so that you can form any whole amount between Re 1 and Rs 100?

Please mail your replies to: kabir.firaque@expressindia.com

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