Why pigeonhole principle?

Will you please elaborate why we are using pigeonhole principle here, and also how would I know that we can use pigeonhole principle in these type of questions??

it is an observation which you will get after attempting question seriously.
pigenhole principle is common sense only not an extra concept

it comes with practice

first you devlope some approach but that will not work due to constraints which are large ,then think of some pattern or something else eventually you will come up with the peigonhole principle

if you have further doubt
feel free to ask

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