The Buddha was travelling through Magadha with around 500 monks. They arrived at a brahmin village called Khānumata, and in this village they stopped at a park called Ambalatthikā.2
In the village of Khānumata, there was a Brahmin named Kūtadanta (meaning "sharp-tooth") who lived on royal property given to him by King Bimbisāra. Kūtadanta decided he wanted to perform a great sacrifice: he had 700 bulls, 700 steers, 700 heifers, 700 goats, and 700 rams tied up, ready to be slaughtered for the ceremony.
Rumors of the Buddha's visit to the park spread quickly through the village. "They say this ascetic is an Arahant, a fully-enlightened Buddha! He is said to teach gods and men alike! We would be very fortunate to be able to see a person like this." A crowd gathered up and they set off for the park.
Kūtadanta had been getting ready to take a nap when he saw the crowd leaving. He called for his steward and asked about what was going on. His steward told him about the Buddha and the crowd's intention to pay him a visit. The Brahmin thought to himself, "I've heard of this ascetic! I've been told he knows how to conduct 'The Sacrifice of 3 Modes With 16 Accessories.'3 Truthfully, I don't understand the details of this practice, but I want to perform a great sacrifice. I should go and ask him to teach me about it."4 He told his steward to go and ask the crowd to wait for him while he got ready.
There were hundreds of other Brahmins staying in the village, and word of Kūtadanta's plans got 'round to them. They went to his property and asked if the rumors were true. When he confirmed, they cried out in protest: "You are a noble Brahmin, and this Gautama is a lowly ascetic! You are a high-born; you are wealthy; you have studied the Vedas; you are handsome; you are ethical; you're a skilled speaker; you have taught many Brahmin students from many places; you're an elder, and this Gautama is still a young man; you're honored by King Bimbisāra as well as the great Brahmin Pokkharasāti; you live in this Brahmin village on royal grounds given to you by the king himself! It would damage your reputation and your livelihood to visit this ascetic. He should honor you by being the one to come and see you."
Kūtadanta objected. "No, Brahmins, you are wrong. Let me explain why! He, himself, is a high-born; he left the noble life behind, abandoning his clan and all of his riches; he made himself a homeless beggar while in the prime of his youth; he resisted the pleas of his parents, and became a wanderer; he is handsome, ethical, a skilled speaker, and a teacher of many, like me; moreover, he has has abandoned desire for sensual pleasures; he teaches the truth about actions and the fruits they produce; he does not wish harm on us Brahmins; he is a holy man from a noble Khattiya family; people from foreign lands come to him for guidance; he has even been a refuge for thousands of gods!"
He continued, "I have heard what people say of him. They say he is an Arahant, a fully-enlightened Buddha; he is perfected in knowledge and conduct; his body bears the 32 Marks of Great Man; among his many devotees are gods and men alike; anywhere he stays is safe from beasts and spirits; he has earned his reputation through his achievement of knowledge and conduct; even King Bimbisāra is a devotee, along with the king's son, wife, followers, and ministers; King Pasenadi of Kosala and the great Brahmin Pokkharasāti are counted among his disciples, as well!"
He concluded, "He has come as a guest in this city to stay in the park. Men like him should be honored and revered, so it is only proper for me to be the one to visit him. I have praised him this much, but even this falls short! Truly, he is beyond all praise."
The Brahmins were moved by this praise for the Buddha, and they decided to tag along and meet him as well. So, a massive crowd of people set out for the park.
When the group reached the Buddha, Kūtadanta exchanged polite greetings with him and sat down to his side. Some of the other people from the crowd also approached the Buddha; some bowed, some exchanged polite greetings, some joined their palms in salutation, and some introduced themselves by announcing their name and their clan. Others simply remained silent.
"Master Gautama," the Brahmin said, "I have heard that you know about 'The Sacrifice of 3 Modes With 16 Accessories.' I want to perform a great sacrifice, but I do not understand all of the details; can you teach me?" The Buddha responded, "Very well. Listen closely, and I will teach you."
The Buddha began telling a story about a king named Mahāvijita, and the time he planned to hold a great sacrifice like the one Kūtadanta wanted to perform. "This king was rich, Brahmin, and his dominion was vast - while reflecting on his situation, he decided to hold a great sacrifice in order to ensure his continued welfare and happiness. He called for his head priest, and told him to offer advice on how to proceed with the ceremony."
"This head priest told the king, 'Your Majesty, your country is plagued with burglars and brigands. Villages and towns are being destroyed. This needs to be addressed. However, raising taxes won't fix anything, and neither will imprisonments, executions, or any such harsh legal punishments. There is only one solution: you must see to it that the material needs of your people are met. Distribute grains and feed to farmers! Ensure merchants have capital! Give living wages to those who work in your government. If you guarantee that people have no want for necessities, they will focus on their occupations, and they will not bring harm to your realm. You will still enjoy riches, and your people will be joyous! They will play with their children, and they will live in open homes.'"
The Buddha continued. "The king followed this advice, and was delighted by the results. He told the head priest, 'It really worked! Now, let's proceed with the ceremony. Tell me what I need to do.' The head priest instructed him to call four groups of people: the Khattiyas; the counsellors in the king's employ; the influential Brahmins; and the wealthy householders. He did so, and all of these people agreed to attend the sacrifice."
"Brahmin, the king had 8 magnificent qualities: he was of noble birth on both sides of his family; he was handsome; he was wealthy; he was powerful, with an army filled with glorious elephants, cavalry, chariots, and infantry; he was a generous host to all classes of people; he was educated; he was wise, and he understood the workings of good fortune in the past, present, and future. These 8 qualities served as accessories of the sacrifice.”
"The head priest had 4 magnificent qualities himself: he was of noble birth on both sides of his family; he knew the mantras and the Vedas; he was virtuous; he was educated, being the first or second to hold the ritual ladle. These 4 qualities also served as accessories of the sacrifice."
"The head priest informed the king that he may have 3 regretful doubts regarding this great sacrifice. 'First, king,' he said, 'before the sacrifice, you may worry that you will lose a lot of wealth. Secondly, during the sacrifice, you may worry that you are presently losing a lot of wealth. Finally, after the sacrifice, you may worry that you have lost a lot of wealth. Your Majesty, you should not pay any mind to these sorts of thoughts."
"Next, the head priest comforted the king regarding doubts the king had about the benefits this sacrifice would have for the people who attended. 'Your majesty,' he said, 'This ceremony will be attended by those who kill living creatures, as well as those who abstain from taking life. Those with blood on their hands will reap what they have sown - you can't fret over them. Instead, you should rest assured that this sacrifice will be of great benefit to those who abstain from taking life. They will rejoice, and feel calmness in their hearts! Do this for their sakes, and be confident that you are benefiting them!"
"He said the same thing regarding these other types of people who would attend the ceremony: those who steal, and those who do not; those who commit sexual misconduct, and those who do not; those who lie, and those who do not; those who speak divisively, and those who do not; those who speak harshly, and those who do not; those who engage in meaningless chatter, and those who do not; those who are covetous, and those who are not; those who have ill-will, and those who do not; and finally, those who have Wrong View, and those who do not."
"Next, the head priest reassured the king about the validity of the sacrifice. He said, 'Your majesty, some people may gossip and disparage you for not inviting the four groups of attendants: the Khattiyas; your counsellors; the influential Brahmins; and the wealthy householders. However, this would not be true, since you certainly invited them! Therefore, rest assured that this sacrifice will be successful. Rejoice, and be calm. Furthermore, some may say that you do not possess the 8 magnificent qualities... and again, some may say that I, your head priest, do not possess the 4 magnificent qualities... Once again I tell you, king, to rest assured - these words would not be true! Rejoice, and be calm."
The Buddha told Kūtadanta that the king's sacrifice was a great success. Not a single animal was slaughtered that day. No trees were felled for sacrifical posts (to which the animals would have been tied). No grasses were cut to be strewn over the area of the sacrifice. Not only were animal lives spared, but even plant life was protected. The only things offered in the sacrifice were ghee, oil, butter, curds, honey, and molasses.
Furthermore, not a single slave or laborer was coerced to work by force. Anyone who helped set up the ceremony did so willingly, and those who helped performed only the tasks to which they felt inclined.
The four groups of people the king had invited to the ceremony were so moved by the sacrifice that they brought many offerings for the king as a show of appreciation. However, when they brought them before King Mahāvijita, he refused to accept them, saying "The taxes paid to me by my people provide anything I could ever need; please, take these offerings back with you, and in addition, take some gifts from my own treasuries!"
These people felt like it would be inappropriate for them to keep all of this wealth for themselves, so they decided to hold their own sacrifices. Each group set up their share of the treasure in one of the four directions of the greater sacrifice, and in their own smaller sacrifices, they also refrained from harming animal or plant life.
The Buddha explained to Kūtadanta that this story demonstrated how 'The Sacrifice of 3 Modes With 16 Accessories' is meant to be performed. The Brahmins who had come to the park cheered and applauded, but Kūtadanta was silent, deep in thought.
Concerned, the Brahmins asked why he didn't applaud for the Buddha's story about the sacrifice. Kūtadanta responded, "It's not that I don't think this is worthy of applause - after all, anyone who wouldn't applaud such a story would have their head split into 7 pieces.5 It's just that... well, I realized Master Gautama did not say anything like 'I have heard,' or 'it must have been this way' while he told his story. This must mean he was speaking from experience. In a past life, he must have been King Mahāvijita, or perhaps the head priest... Master Gautama, is this true?"
The Buddha confirmed. "Yes, Brahmin, you are correct. In that time, I was the high priest who instructed the king."
"Master Gautama," the Brahmin asked, "is there a sacrifice which is simpler and more beneficial than this 'Sacrifice of 3 Modes With 16 Accessories'?" The Buddha replied, "Yes, there is." Kūtadanta asked him to explain.
"When ordinary offerings are given regularly to virtuous ascetics by families," the Buddha said, "this is a sacrifice which is simpler and more beneficial than the grand sacrifice." When Kūtadanta asked why this is the case, the Buddha explained that arahants and those who are training to become arahants would not attend grand sacrifical ceremonies because of the violence which occurs - specifically, beatings and throttlings (presumably of the slaves and common laborers). These holy people would attend the simple offerings held regularly by families, however.
This dialogue goes back and forth between the Buddha and Kūtadanta, with the Buddha providing 6 more examples of these symbolic, metaphorical sacrifices, each being "simpler and more beneficial" than the last.6 These include: providing shelter for travelling members of the sangha; going confidently to the Buddha-refuge, the Dhamma-refuge, and the Sangha-refuge (or, in basic terms, converting); confidently taking the 5 basic ethical precepts (no killing, no stealing, no sexual misconduct, no sexual immorality, no intoxication).
The rest of the examples given by the Buddha appear in the form of the Sīlakkhandhavagga Pericope. The Buddha discusses the appearance of a Tathāgata and begins the next example with "Someone Gains Faith" and ends it with the First Jhāna. The next example covers the 2nd through 4th Jhānas. The next example covers "Insight Through Samādhi" through the attainment of the "Divine Eye." Finally, the Buddha concludes with the destruction of the defilements and the attainment of enlightenment, culminating in one's knowledge they will not return to any state of existence.
Kūtadanta once more asked if there were a sacrifice simpler and more beneficial than this, and the Buddha said, "No, there is no other sacrifice which is simpler and more beneficial."
Kūtadanta praised the Buddha, and declared himself a lay disciple. He released all of the animals which he had planned to slaughter for the sacrifice. The Buddha taught him the Dhamma, step-by-step, beginning with generosity, and progressing through ethics, a discussion of the heavenly realms, the dangers of sense-pleasures, and the benefits of renunciation. When the Brahmin's mind was ready, the Buddha taught him the Four Noble Truths. Kūtadanta attained the Dhamma-eye; he experienced the insight that all things which arise must pass away.
He invited the Buddha and his monks to attend a meal offering at his residence the following day. The Buddha consented in silence, as was his custom, and the Brahmin left. He had the food prepared where he had planned to hold the great sacrifice, and when it was ready, he called for the sangha. When they arrived, he served them with his own hands. After the Buddha had finished eating, Kūtadanta sat down below him and to his side. The Buddha gave him another teaching, and it filled the Brahmin with inspiration and determination. After this, the Buddha rose up and walked away.
The corresponding sutra from the Chinese Canon is Dīrghāgama 23. I do not have access to a translation of the sutra, so I cannot provide a comparison. I will try to update this section if I ever get the chance.
 This sutta bears striking similarities to DN 4. I won't bother pointing out each parallel, because they're so frequent and obvious to anyone who has read both. Accordingly, I have simply copied and pasted some of my previous synopsis. If the monks who compiled the Pali Canon can do it, so can I!
 In the commentary, Buddhaghosa points out that this is a different park than the one mentioned in DN 1 despite bearing the same name and being described similarly.
 This numbering will be explained later. For now, don't worry about it, it isn't a terribly important detail.
 Walshe, in his translation of this sutta, cites Rhys Davids in pointing out that this story is most likely a fabrication. The idea of a Brahmin priest consulting a non-Brahmin ascetic on how to perform a Vedic sacrifice is, on its face, nonsensical. Furthermore, in the Yañña Sutta (SN 3.9), there is a (presumably historical) story about a similar sacrifice being prepared for King Pasenadi of Kosala (on his orders).
In that sutta, the Buddha told some of his monks that such sacrifices are worthless and violent, and preached instead on the simpler types of symbolic sacrifices - acts of religious devotion - which are better. The verses of this short sutta are quite similar to the points of this longer story in the Digha Nikaya. It doesn't take a great leap of the imagination to entertain the possibility that the shorter sutta served as an inspiration for this longer story. I believe this suspicion is only strengthened by the fact that much of this sutta mirrors DN 4.
This suspicion is no reason to discard this sutta entirely, however. It is entirely possible that the sermon portion of this sutta legitimately stems from a teaching given by the Buddha, and its core message is certainly one worth hearing regardless of the narrative framework.
 For more details on this strange line, see the second disclaimer in mysynopsis for DN 4.
 Truthfully speaking, I don't understand what makes each progressive example "simpler" than the one that comes before it. More beneficial, sure, but I can't help but feel like making offerings to the sangha is a simpler ordeal than destroying the mental defilements and attaining nibbana. Ultimately, this is a small detail and probably isn't worth reading into too much.