IMO 1962, Problem 1 · Number Theory
IMO 1962, Problem 1
Find the smallest natural number with the following properties: its decimal representation ends in the digit , and if that final is erased and placed in front of the remaining digits, the resulting number is four times .
This is a proof problem. The answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.
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Train it on Lemma
This problem sits in the Olympiad Set: 89 proof problems (real IMO problems and the classics) with progressive hints, full walkthroughs and marking rubrics. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.
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