PIMSO 2022 - Mathematics - Grade 2 - National Round

N is a 3-digit number such that all digits are divisible by a common whole number that is not 1, but all digits are also different from each other. What is the maximum possible value of N?

“A” is 102 more than 51 and “B” is 72 less than 99. What is A+B?

What is the sum of all counting numbers from 1 to 50?

What three consecutive counting numbers have a sum of 300?

Input format (editorial): enter the numbers in increasing order, separated by commas.

If $\frac{N}{20}-\frac{3}{15}=\frac{6}{10}$, what is the value of N?

What is the remainder when the answer in #5 is divided by 3?

At the end of a meeting, four students shake hands with each other once. How many handshakes will be there altogether?

It is Leta’s birthday today. She is 5 years older than Leo. If you add their ages the sum is 27. How old is Leta?

What is next in the series?

Four moons – Deimos, Ganymede, Phobos, Titan – were talking to each other and comparing their sizes.

Titan said “I am bigger than Phobos.”
Deimos said “Ganymede is bigger than Titan.”
Phobos said “Titan is bigger than Deimos.”
Ganymede said “Phobos is bigger than Deimos.”

Which moon is the largest?

A clock shows 6:00 AM. If the minute hand points in the direction of west, then in which direction is the hour hand pointing?

If [Monday → Saturday] and [Wednesday → Monday], then [Thursday → ____?____ ]

Find the number F if $F\times17\times257=21{,}845$.

Find the number F if $F\times5\times17=850$.

Simplify:
$1{,}012+2{,}013+3{,}014+4{,}015+5{,}016+6{,}017+7{,}018+8{,}019+9{,}020+10{,}021+11{,}022+12{,}023$.

Simplify $18{,}007-17{,}009+16{,}011-15{,}013+14{,}015-13{,}017+12{,}019$.

Simplify: $109+98+87+76+65-59-48-37-26-15$.

Find the number R if $R>F$ and $(R\times F\times23)=12{,}121$.

TRUE, FALSE, or SOMETIMES: All squares are rectangles.

How many small squares with width 2 cm can you cut out from a big square with width 10 cm?