This is the third IOQM Mock test from MOMC. The problems are collected from PuMaC 2018 and CHMMC 2014. All the credit and authorship of the problems belongs to their respective sources.

I felt for a long time that there was no difficulty scale to express the difficulty of problems in IOQM or any other computational exam. So I decided to make one myself. Therefore I present to you- CODS (Computational Olympiad Difficulty Scale)! A difficulty scale ranging from 1-6 for IOQM 5 markers. As the 2 and 3 markers are no big deal, there is no point in making a difficulty scale for them. Hence this scale is only for 5 markers.

**Rating 1: Very Doable.** Problems rated 1 are very doable 5 markers. An example is:

- IOQM 2022 P18 on LCM and GCD

**Rating 2: Mostly Doable.** Problems rated 2 are manageable. However, they aren't trivial and require some effort. Some examples are:

- IOQM 2022 P20 on Landmark Points
- IOQM 2022 P21 on 1 Hour Journeys of an Ant

**Rating 3: Moderate.** This is the rating at which students start facing some difficulty. Some examples are:

- IOQM 2022 P16 on System of equations
- IOQM 2022 P17 on $f(f(f(N)))=97$

**Rating 4: Challenging.** Problems of rating 4 form the more challenging end of the 5 markers. Most students cannot solve these. An example is:

- IOQM 2022 P14 on $\frac{x}{y+z} + \frac{y}{z+x} + \frac{z}{x+y} = 9$

**Rating 5: Very Challenging.** These are the hardest 5 markers that can be found in IOQM. Only a handful of students are able to solve these problems in the exam. Some examples are:

- IOQM 2022 P13 on $AD= BC$ and angles in arithmetic progression
- IOQM 2022 P22 on friendly binary sequences

**Rating 6: Unsuitable.** It's unlikely that such a difficulty will appear in the real IOQM, but you might encounter it in my mocks.

Here are some examples of ratings for this particular mock and previous mocks:

## Apple Mock 1

P21 | P22 | P23 | P24 | P25 | P26 | P27 | P28 | P29 | P30 |
---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 3 | 5 | 3 | 4 | 3 | 3 | 4 |

## Apple Mock 2

P21 | P22 | P23 | P24 | P25 | P26 | P27 | P28 | P29 | P30 |
---|---|---|---|---|---|---|---|---|---|

3 | 5 | 4 | 1 | 2 | 4 | 3 | 4 | 1 | 4 |

## Apple Mock 3

P21 | P22 | P23 | P24 | P25 | P26 | P27 | P28 | P29 | P30 |
---|---|---|---|---|---|---|---|---|---|

3 | 5 | 5 | 2 | 1 | 1 | 3 | 4 | 4 | 5 |