John is a strange liar

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?




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When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

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In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.