Sub-topic 1
2025 · National One-Eighth
Free
Expressing $193$, $145$ and $157$ as sums of two squares of natural numbers
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Sub-topic 2
2026 · National Preliminary
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Expressing $125$ as the sum of two square numbers
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Sub-topic 3
2025 · National One-Eighth
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Riddle: identifying a three-digit number from digit clues
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Sub-topic 4
2024 · National One-Eighth
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Riddle: an odd square between $100$ and $200$ with a prime base
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Sub-topic 5
2024 · National One-Eighth
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Riddles identifying prime numbers from their divisibility property
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Sub-topic 6
2025 · National Semifinal
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Counting the odd three-digit palindromes $\overline{aba}$ whose digits sum to $11$
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Sub-topic 7
2024 · National One-Eighth
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Verifying congruences such as $15\equiv-13\pmod{14}$ (true/false)
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Sub-topic 8
2024 · Regional Championship
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Divisibility of the factors when the product $mn$ is divisible by $4$ (true/false)
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Sub-topic 9
2024 · Regional Championship
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Riddle: identifying a year (four-digit number) from digit-sum and primality clues
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Sub-topic 10
2023 · National Preliminary
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Riddle: $1357$ from digit-identity and arithmetic-sequence clues
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Sub-topic 11
2023 · National Preliminary
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Riddle: the number $2$, the only even prime
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Sub-topic 13
2003 · National Semifinal
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Finding the base $b$ for which $732-81=661$
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Sub-topic 14
2003 · National Semifinal
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Clock time $42$ hours after eight o'clock (modular arithmetic)
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Sub-topic 15
2003 · National Semifinal
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Clock time $63$ hours after four o'clock (modular arithmetic)
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Sub-topic 16
2003 · National Semifinal
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Riddle: an exact square whose reverse is $12^2$ and whose digit sum is divisible by $9$
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Sub-topic 17
2012 · National Preliminary
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Finding the base $n$ when $34_n=28_{10}$
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Sub-topic 18
2012 · National Preliminary
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Finding the base $n$ when $57_n=67_{10}$
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Sub-topic 19
2013 · National Quarterfinal
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Finding $n$ in $(3\times10^5)\div(8\times10^{-3})=3.75\times10^n$
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Sub-topic 20
2013 · National Quarterfinal
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Finding $n$ in $(7.5\times10^{-4})\div(0.25\times10^{-7})=3.0\times10^n$
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Sub-topic 21
2013 · National Quarterfinal
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Standard form of $0.0000325\times10^{-7}$
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Sub-topic 22
2014 · National Quarterfinal
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Finding the base $n$ when $215_n-126_n=56_n$
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Sub-topic 23
2014 · National Quarterfinal
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Finding the base $n$ when $215_n+126_n=343_n$
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Sub-topic 24
2014 · National Quarterfinal
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Finding the base $n$ when $315_n+574_n=1000_n$
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Sub-topic 25
2016 · National One-Eighth
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Finding the next prime number after $173$
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Sub-topic 26
2016 · National One-Eighth
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Riddle: a two-digit even number with prime digits differing by $5$
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Sub-topic 27
2016 · National One-Eighth
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Counting the significant figures in $350$
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Sub-topic 28
2018 · National Preliminary
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Riddle: a four-digit odd palindrome $abba$ where $b^2=a$
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Sub-topic 29
2019 · National Preliminary
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Finding the prime numbers between $80$ and $90$
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Sub-topic 30
2019 · National Preliminary
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Finding the base $n$ when $123_n=38_{10}$
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Sub-topic 32
2023 · National Preliminary
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Riddle: $1089$, a four-digit odd number with digit sum $18$
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Sub-topic 33
2023 · National Preliminary
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Riddle: the number $2$, the only even prime that partitions the integers
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Sub-topic 34
2023 · National Preliminary
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Riddle: $1357$, digits forming an arithmetic sequence of primes starting from $1$
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Sub-topic 35
2023 · National Preliminary
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If $a+b$ is even, are $a$ and $b$ both even? (true/false)
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Sub-topic 36
2023 · National Preliminary
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If $ab$ is odd, are $a$ and $b$ both odd? (true/false)
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Sub-topic 37
2023 · National Preliminary
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If $ab$ is even, is at least one of $a$, $b$ even? (true/false)
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Sub-topic 38
2023 · Regional Championship
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Riddle: $48$, a two-digit number with digit sum $12$ where one digit divides the other
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Sub-topic 41
2025 · National Preliminary
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Expressing $265$ as a sum of two squares
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Sub-topic 41
2024 · National One-Eighth
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Riddle: an odd square between $100$ and $200$ whose square root is prime
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Sub-topic 42
2026 · National Preliminary
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Riddle: a three-digit odd number between $100$ and $200$ with last digit $7$ and digit sum $11$
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Sub-topic 43
2025 · National Quarterfinal
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Expressing $29$ as a difference of two squares
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Sub-topic 44
2026 · National Preliminary
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Expressing $29$ as a difference of two squares (second contest)
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Sub-topic 45
2024 · National One-Eighth
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Expressing $43$ as a difference of two squares
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Sub-topic 46
2026 · National One-Eighth
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Expressing $47$, $61$ and $71$ as differences of two squares
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Sub-topic 47
2025 · National One-Eighth
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Riddle: a three-digit number between $300$ and $400$ from square-digit clues
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Sub-topic 48
2023 · National One-Eighth
Premium
Riddle: $729$, an odd three-digit number that is both a square and a cube
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