PIMSO 2022 - Mathematics - Grade 3 - National Round

N is a 4-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 the remainder when A is divided by B?

What is the minimum 3-digit number such that the tens digit is divisible by the ones digit, the tens digit is higher than the hundreds digit by 2, and the sum of the hundreds and the ones digits is 10?

What three consecutive odd integers have a sum of 249?

Enter the three integers in increasing order, separated by commas.

Sequence S begins with 1, followed by terms which are the results of multiplying 2 to the preceding number. What is the 11th term of the sequence?

Given the problem in #5, if S is a series, what would be its sum up to its 11th term?

Context from Question 5: S starts at 1 and each following term is twice the preceding term.

It is Leta’s birthday today. She is 5 years older than Leo. If you multiply their ages the product is 176. Find the sum of their ages.

Cecilia, Dina, Elena, and Fiona are cousins with different ages who live in the same house. When a new neighbor asked them who is the oldest, they answered: Cecilia: I am the eldest. Dina: I am not the youngest. Elena: I am neither the eldest nor the youngest. Fiona: I am the youngest. Given that one of them is not telling the truth, who is the oldest of the four cousins?

It is Leta’s birthday today. She is 5 years older than Leo. If you multiply their ages the product is 546. Find the sum of their ages after 3 years from today.

What is the missing number?

What is the next number in the series?

16, 21, 12, 18, 10, 17, 8, ___

Pattern convention (editorial): group consecutive terms into pairs and continue the second-minus-first differences by increasing them by 1.

A clock shows 4:30 AM. If the minute hand points in the direction of west, then in which direction is the hour hand pointing?

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

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

If F is a counting number between 0 and 10, R is a whole number and $R>F$, find F if: $11+(R\times22)=(F\times6)+(F\times27)$ and $R-F=1$.

Simplify: $19{,}109+18{,}098+17{,}087+16{,}076+15{,}065-14{,}059-13{,}048-12{,}037-11{,}026-15$.

Simplify: $14{,}111+13{,}212+12{,}313+11{,}414+10{,}515+9{,}616+8{,}717+7{,}318+6{,}419+5{,}520+4{,}621+3{,}722+2{,}823+1{,}924$.

Simplify: $211+212+213+214+215+216+217+218+219+220+221+222+223+224$.

Trevor conditions himself every morning by walking 10 full laps along a circular track for exactly an hour a day. If the diameter of the track is 60 meters, how many kilometers would he have walked in 10 days? (Use π=3.14)

Trevor is joined by his friend, William, in his morning exercise. They both begin at the same point and time, then they walk towards opposite directions along a circular track with a radius of 100 meters. If the rate of Trevor’s pacing is twice as fast as William’s, how many meters would Trevor have walked by the time William reaches the opposite side of the starting point on the circle? (Use π= 3.14)