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Erdős problem 202

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Let n1<⋯<nr≤Nn_1<\cdots < n_r\leq N with associated ai(modni)a_i\pmod{n_i} such that the congruence classes are disjoint (that is, every integer is ≡ai(modni)\equiv a_i\pmod{n_i} for at most one 1≤i≤r1\leq i\leq r). How large can rr be in terms of NN?

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Problem row
sha256:5a36d706b12d828f3cfb9b8b33e56720ef6b09c250b89eb9dda009b6fe8175ca
Metadata
sha256:89039205f4822691ba5697499250d49758ef955a444ad085e5582ce57c1f8e1b
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:2651d4a0591251fc3c0dca4e25453bd1e0013a4ad348ee72f09d7491d9fd03d7
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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