A farmer must cross a river with a fox, a chicken, and a bag of grain

Why

Yash's instinct comes from noticing that TWO different pairs are dangerous, which can feel like there is no safe order at all — but the trick is realising the chicken is the one item involved in BOTH dangerous pairs, so carrying it back and forth solves both problems. Take the chicken across first (fox and grain are safe left together, since a fox has no interest in grain). Go back alone. Take the fox across — but now fox and chicken would be alone together, so bring the chicken back with you instead of leaving it. Take the grain across, leaving it safely with the fox. Go back alone one last time, and take the chicken across. Test it: at every single step, check what is left alone on each bank — fox+grain (safe), chicken alone (safe), fox alone (safe), chicken+grain (safe) — the chicken is never left with the fox or the grain unsupervised at any point. His teacher is right: everyone crosses safely in 7 trips across the river — the key insight is realising which single item is the source of both risks, and keeping that one under control by moving it back and forth.