New Zealand Maths Olympiad Competition (NZMOC) Update

On August 30th, Naoki participated in the second round of the New Zealand Olympiad Competition, having qualified after his success in the first round.

Round 2 consisted of a 3-hour written exam, where Naoki was required to solve 5 problems, each carrying equal marks. Detailed written solutions and complete proofs for any assertions made were expected. His score would reflect the clarity of his mathematical presentation, so he was encouraged to work out rough drafts before finalising a polished version of his best attempts.

Naoki earned a Bronze award for his efforts in this challenging competition, with awards distributed in an approximate ratio of 1:2:3 for gold, silver, and bronze.

An example of the question:

At each vertex of a regular 14-gon, lies a coin. Initially 7 coins are heads, and 7 coins are tails. Determine the minimum number t such that it’s always possible to turn over at most t of the coins so that in the resulting 14-gon, no two adjacent coins are both heads and no two adjacent coins are both tails.

The results from rounds 1 and 2 are combined to select approximately 30 students who will be invited to the annual NZMOC Training Camp, scheduled for January 2025. We wait in anticipation to see whether Naoki has been selected to attend.