Rabbi Eliezer says: “A person has no absolute obligation on Yom Tov; rather, he may eat and drink or he may sit and study Torah.”
Rabbi Yehoshua says: “Divide the day into two parts – part of it should be devoted to eating and drinking, and part of it to Torah study.”
Rabbi Yochanan said: “And they both expounded the same text in reaching their conclusions as follows:
“One verse states: ‘there shall be an assembly to Hashem your God ’ (implying one should study God’s Torah on Yom Tov) and another verse states: ‘there shall be an assembly for you ’ (implying one should observe the festival by partaking of physical delights).
“Rabbi Eliezer maintains that one may therefore decide whether to devote Yom Tov either exclusively to God or exclusively to yourselves; whereas Rabbi Yehoshua maintains that one should apportion the day between God and yourselves.” (Gemara Pesachim 68b)
The Vilna Gaon pointed out a stunning Gimatriya  on this topic. Rabbi Yehoshua said to divide the day into two parts – part of it (chetzyo) should be devoted to you (lachem), and part of it (chetzyo) to God (laHashem). The Gimatriya of the word “lachem” is 90 (lamed is 30, chaf is 20 and mem is 40). The Gimatriya of the word “laHashem” is 56 (lamed is 30, yud is 10, hei is 5, vav is 6 and hei is 5). Therefore, half (chetzyo) of “lachem” is 45 and half of “laHashem” is 28. This is how Rabbi Yehoshua taught us to spend Yom Tov, whose Gimatriya is 73 (yud is 10, vav is 6, mem is 40, tet is 9, vav is 6 and vet is 2) = 45 + 28!
Interestingly, Maharshal  warned chazanim not to drag out the prayers unnecessarily with chazanut on Yom Tov, even if their intention is noble, and even if the congregation approves. This is neither the “chetzyo lachem” nor the “chetzyo laHashem” that our Sages intended.
Rabbeinu David wonders whether the continuation of our Gemara supports Rabbi Eliezer’s approach. We learn that Mar, the son of Ravina, would fast even on Yom Tov (with the exception of Shavuot ). Clearly, Mar followed Rabbi Eliezer’s opinion, by devoting his entire Yom Tov to Torah and prayer.
Rabbeinu David explains, however, that unique individuals such as Mar are so immersed in their Torah study that they take physical pleasure in it, no less than the pleasure we experience when eating a festive meal. They are able to fulfil both the “half for God” and the “half for yourselves” at once, by learning Torah. Therefore, they have no need to eat on Yom Tov. However, we cannot apply this as a general rule for others.
1. Devarim 16:8
2. BeMidbar 29:35
3. Gimatriya provides a method of converting Hebrew letters into numerical values.
4. Cited in Shaar HaTZiyun to Mishnah Berurah 529:1
5. By feasting on Shavuot he would demonstrate that he