The Emperor’s Triangular Array
To emulate and surpass the famous emperor Qin’s necropolis achievement, emperor Wu Shu, who preferred to be known as “He Who Cannot Be Counted,” decided that after the end of his life he wanted to be buried at the head of an army of 10,440 terracotta soldiers standing at attention in a triangular array of rows.
“Chow Sao, I want to know the cumulative Grand Sum of the number of ways of arranging soldiers in each respective row,” said emperor Wu Shu to his Feng Shui advisor.
“This Grand Sum must be perfectly divisible by 12, the number of heavenly animals in the Shengxiao zodiac,” added emperor Wu Shu.
“Yes, my glorious emperor,” moaned Chow Sao, “your wish is my command,” starting to genuflect reversing himself out of the emperor’s lush palace quarters.
“If the Grand Sum is not perfectly divisible by 12, I want you to tell me exactly which rows of soldiers must be removed to obtain a zero remainder,” commanded emperor Wu Shu.
“As you wish, my illustrious emperor,” said Chow Sao, shuffling more rapidly to increase his reverse velocity as he saw empress Soo Lao enter the palace room.
“This grand sum must be perfectly divisible by 12. Empress Soo Lao has informed me that I shall suffer great misfortune in the heaven life unless this is so,” emphasized emperor Wu Shu, waving his scepter.
“This is so, Chow Sao,” said empress Soo Lao sternly, “any mistakes, and I will have sorceress Ba Fa turn you into stone and place you as the first soldier in the first row.”
“The Gods forbid,” said Chow Sao accelerating his backward velocity at a phenomenal rate and absconding from the emperor’s quarters in a great hurry to begin his calculating task.
Would you say that this Grand Sum was divisible by 12, and if not, would any rows of soldiers have to be removed from the triangular array of soldiers envisioned?
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