Mathematik-Olympiade preparation in English

1. Ask the maths teacher at the start of the school year whether the school runs the Schulrunde, and how.
2. Solve the Schulrunde. It is usually done at home, sometimes as a paper in school. In primary schools the school decides the format, alone or in groups.
3. Sit the Regionalrunde if invited. In the 66th olympiad it is on 11 November 2026, with four problems at a central place.
4. Go on to the Landesrunde at the end of February if selected: 26 to 28 February 2027 in this round.
5. From Klasse 8, the Bundesrunde for the Land's team: 30 May to 2 June 2027 in Kaiserslautern.

Source: Bundesweite Mathematik-Wettbewerbe, Mathematik-Olympiade FAQ on mathe-wettbewerbe.de/mo, read on 3 November 2026.

def digit_sum(n):
    return sum(int(d) for d in str(n))

# Problem A: three-digit numbers whose digits add up to 5
print("A:", sum(1 for n in range(100, 1000) if digit_sum(n) == 5))

# Problem B: smallest n > 9 with the same digit sum as 2n, and a check on 9
balanced = [n for n in range(10, 100000) if digit_sum(n) == digit_sum(2 * n)]
print("B:", balanced[0], "all divisible by 9:", all(n % 9 == 0 for n in balanced))

# Problem C: n*n + 3n + 5 for n = 1 to 10000
f = [(n, n * n + 3 * n + 5) for n in range(1, 10001)]
by_11 = [n for n, v in f if v % 11 == 0]
print("C: divisible by 11:", len(by_11), "all with n % 11 == 4:", all(n % 11 == 4 for n in by_11))
print("C: divisible by 121:", sum(1 for n, v in f if v % 121 == 0))

The program agrees with all three solutions, which is reassuring. But look at what it actually did: it tested the numbers 1 to 10,000 for Problem C and found none divisible by 121. That cannot rule out a larger number, and an olympiad marker would give no credit for it. The algebra above covers every whole number at once. We use small programs like this in class for one purpose only: to test a guess before trying to prove it, and to catch an arithmetic slip in a solution. In the olympiad itself, as in any written paper, there is no computer and the proof is the whole answer.

1. Extend A. How many four-digit numbers have digits adding up to 5? Predict first, then check with one change to the program.
2. Test B. Find the five smallest balanced numbers above 9 by hand, then compare with the program's list.
3. Vary C. For which n is n² + 5n + 7 divisible by 3? Write the full solution before running any code.
4. Explain. In two sentences, say why 909 numbers from 1 to 10,000 leave remainder 4 on division by 11.

German time under the Einheitenzeitgesetz is UTC+1 in winter and UTC+2 in summer. The switch back to winter time came on 25 October 2026; summer time returns on 28 March 2027. India runs on UTC+5:30 without any change, four and a half hours ahead of Germany in winter and three and a half in summer.

The rows are examples only, never a promised batch time. Around the Regionalrunde and the Landesrunde, one-to-one pupils often add a session of written practice under time pressure.