## Practice Problems

If the embedded PDF Viewer is not working on your browser, the 2023 Practice Problems can also be downloaded here.

Until the start of the contest at October 2023, https://cms.noi.ph/ leads to the TAMa Practice Round, where you can submit your answers to these problems using the contest interface.

## Answers

Again, until the start of TAMa itself, https://cms.noi.ph/ leads to the TAMa Practice Round where you can test your answers using the contest interface.

You can also check the correctness of your solutions by comparing them against the answers here. During the actual contest, an automated checker will handle this step.

**Sum of Sum of Odds: **Answers

**Mod Powers: **Answers

**Summer SEMs: **Answers

## Solutions

First, almost all TAMa problems involve modulo because of the size of the numbers involved. You can refer to a quick crash course in modular arithmetic here.

Second, the solution sketches detail solutions for **all four subtasks **in order to 1) let the necessary ideas build on one another naturally, and 2) emphasize that despite later subtasks being possibly quite difficult, it should still be possible to earn points in earlier subtasks using basic mathematics and programming.

We don’t expect you to implement four programs, one for each subtask. Usually, the most efficient program which solves the final subtask can also just be used to solve the other subtasks as well.

**Sum of Sum of Odds: **Solution

**Mod Powers: **Solution

**Summer SEMs: **Solution

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