# AoPS Wiki:Competition ratings

This page contains an approximate estimation of the difficulty level of various competitions.

If you have some experience with mathematical competitions, we hope that you can help us make the difficulty rankings more accurate. Currently, the system is on a scale from 1 to 10 where 1 is the easiest level, i.e. early AMC problems and 10 is hardest level, i.e. China IMO Team Selection Test. When considering problem difficulty put more emphasis on problem-solving aspects and less so on technical skill requirements.[1]

## Voting

### AMC 8

• Problem 1 - Problem 12: 1
• Problem 3 - Problem 25: 2

### AMC 10

• Problem 1 - 5: 1
• Problem 6 - 22: 2
• Problem 18 - 25: 3

### AMC 12

• Problem 1-5: 2
• Problem 3-18: 3
• Problem 22-25: 4

### AIME

• Problem 1 - 5: 3
• Problem 5 - 10: 4
• Problem 11 - 15: 5
• Problem 14 - 15: 6

### ARML

• Individuals, Problem 1-5,7,9: 3
• Individuals, Problem 6,8: 4
• Individuals, Problem 10: 6

### HMMT

• Individuals, Problem 1-5: 4
• Individuals, Problem 6-10: 5

• Problem 1: 4
• Problem 2: 5
• Problem 3: 5
• Problem 4: 6

### USAMO

• Problem 1/4: 5.5
• Problem 2/5: 7
• Problem 3/6: 8.5

### USA TST

• Problem 1/4/7:
• Problem 2/5/8:
• Problem 3/6/9:

### China TST

• Problem 1/4:
• Problem 2/5:
• Problem 3/6: 8

### IMO

• Problem 1/4: 6.5
• Problem 2/5: 7.5
• Problem 3/6: 9

### Miklós Schweitzer

• Problem 1-3:
• Problem 4-6:
• Problem 7-9:
• Problem 10-12:

## Subjective

### AMC 8

• Problem 1 - Problem 12:
• Problem 3 - Problem 25:

### AMC 10

• Problem 1 - Problem 12:
• Problem 3 - Problem 25:

### AMC 12

• Problem 1 - Problem 12:
• Problem 3 - Problem 25:

### AIME

• Problem 1 - Problem 5: 4
• Problem 5 - Problem 10: 5
• Problem 11 - Problem 15: 6

• Problem 1: 4
• Problem 2: 5
• Problem 3: 5
• Problem 4: 6

### USAMO

• Problem 1/4: 4.5
• Problem 2/5: 6
• Problem 3/6: 7.5

### IMO

• Problem 1/4: 5.5
• Problem 2/5: 6.5
• Problem 3/6: 8

### China TST

• Problem 1/4:
• Problem 2/5:
• Problem 3/6: 8

### Miklós Schweitzer

• Problem 1-3:
• Problem 4-6:
• Problem 7-9:
• Problem 10-12:

## Scale

[1]All levels estimated and refer to averages. The following is a rough standard based on the USA tier system AMC 8 – AMC 10 – AMC 12 – AIME – USAMO, representing Middle School – Junior High – High School – Challenging High School – Olympiad levels. Other contests can be interpolated against this.

1. Problems strictly for beginners, on the easiest elementary school or middle school levels. Examples would be MOEMS, easy Mathcounts questions, #1-20 on AMC 8s, very easy AMC 10/12 questions, and others that involve standard techniques introduced up to the middle school level
2. For motivated beginners, harder questions from the previous categories (hardest middle-school level questions, #5-20 on AMC 10, #5-10 on AMC 12, easiest AIME questions, etc).
3. For those not too familiar with standard techniques, #21-25 on AMC 10, #11-20ish on AMC 12, #1-5 on AIMEs, and analogous contests.
4. Intermediate-leveled problem solvers, the most difficult questions on AMC 12s (#22-25s), more difficult AIME-styled questions #6-10
5. Difficult AIME problems (#10-13), others, simple proof-based problems (JBMO etc)
6. High-leveled AIME-styled questions, not requiring proofs (#12-15). Introductory-leveled Olympiad-level questions (#1-4s).
7. Intermediate-leveled Olympiad-level questions, #1,3s that require more technical knowledge than new students to Olympiad-type questions have, easier #2,4s, etc.
8. High-level difficult Olympiad-level questions, eg #2,4s on difficult Olympiad contest and easier #3,6s, etc.
10. Problems occasionally even unsuitable for normal grade school level competitions due to being exceedingly tedious/long/difficult (eg very few students are capable of solving, even on a worldwide basis), or involving techniques beyond high school level mathematics.

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