IMC 2025 Grade 2 — Grand Final

Find $69+7+50+31+53=\underline{\qquad}$.

Find the 35th and the 50th patterns in the sequence.

Fill in the appropriate numbers in the parentheses: $1,1,1,(\quad),5,25,125,7,49,343,9,81,729,11,121,1331,\ldots$

If the model on the right is colored, there are a total of ______ faces without color.



Editorial clarification for grading: assume the model is a solid stack with no gaps and that all outside faces, including the underside, are painted.

Sam has four of each of 1-dollar, 2-dollar and 10-dollar coins respectively and two 20-dollar notes. He buys a 45-dollar piece of clothing. How many different payment methods require no change?

March 4th of a leap year is Monday. What was the date and the day of the week 32 days ago?

Peter saves his pocket money by saving 1 dollar every Monday; 2 dollars every Tuesday; 3 dollars every Wednesday; ...; 7 dollars every Sunday. He started saving on Friday, August 1st. How much has he saved this month?

Four people, A, B, C, and D, are lining up. A is behind C; A is in front of B; and D is at the front. Arrange them from front to back.

Calculate $9-36-88-125-12-94+291+73+5+127=\underline{\qquad}$.

Calculate $2\times3\times4-4\times5\times6-5\times6\times7+8\times9\times10=\underline{\qquad}$.

Fill the blank: $\underline{\qquad}+93+15+47=500$.

Find the value of the final blank. The same flower has the same value each time.



Editorial clarification for grading: the flower values are positive whole numbers.

Use 0, 2, 3 and 5 to form all appropriate two-digit numbers without digit repetition. Find the sum of those numbers.

There are 150 number cards in a bag, with 001–150 written on them. In the worst case, at most how many cards will be drawn and still no card with the digit “0” on it?

The weight of 3 bags of rice is equal to 30 kilograms plus the weight of 2 bags of rice. 10 bags of rice weigh ______ kilograms.

Editorial clarification for grading: all bags of rice have equal weights.

The well is 12 meters deep. The snail climbs up 4 meters during the day and slides down 2 meters at night. In how many days will the snail reach the wellhead?

This year, the elder brother is 12 years old and the younger brother is 7 years old. How old will each brother be when the sum of their ages is 35? Show your reasoning.

Printed scoring note: each Part III question is worth 10 points; a simplified solution is required and is worth 4 of those points.

The elder sister and the younger sister played “rock-paper-scissors” three times. Each win moves them up 2 stairs; each loss moves them down 1 stair. They both started on the 5th stair. Finally, the elder sister won 2 times and the younger sister won 1 time.

(a) How many steps apart were they at the end of the game?

(b) On which step were the two sisters respectively? Show your reasoning.

Printed scoring note: each Part III question is worth 10 points; a simplified solution is required and is worth 4 of those points.