AMO 2027 Grade 2 SET 4 - Self-study

How many rectangles of any size are in the original figure? Count rectangles whose four sides are completely drawn, including the outer boundary and squares.



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Five years ago, the sum of a couple’s ages was 76. Fifteen years later, the man will be 4 years older than the woman. What will their total age be 30 years later? Here “later” means from the present time, as in the source solution.



Enter one whole number, without units.

Count the triangles in the picture. Editorial interpretation for this imperfect drawing: treat the two very close left vertical strokes as one line, and the nearly coincident bottom strokes as one straight baseline. Ignore line thickness and small printing offsets. The left triangle ends before the rectangle’s right side, as shown; do not extend its sloping side.



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Luna had 56 bows. Her friend said, “If you give me 18 bows, I will have double the number of bows you will have.” How many bows did her friend have?

Enter one whole number, without units.

Harry wrote $1,2,3,11,22,33,111,222,333,\ldots$ until he got 17 numbers. What is the sum of the digits of the last number he wrote?

Enter one whole number, without units.

Veena watches a movie on Netflix. She stops after watching one-third of it. If she had watched 12 minutes more, she would have watched half of the movie. How long is the movie, in minutes?



Enter one whole number, without units.

How many whole numbers less than 300 have digits that add up to 5?



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What is the greatest three-digit number divisible by both 5 and 11?



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Suppose today is 15th August, Friday. How many Sundays will there be as of 30th October?

**Editorial note:** Use the stated hypothetical calendar, not the actual 2027 calendar. Count Sundays after 15 August through 30 October inclusive. Choose one option.

Patrick started jumping every day. He jumped 10 times on Day 1, then 8 more times on Day 2 than on Day 1, and 8 more times on Day 3 than on Day 2. Each day he continued to jump 8 more times than the previous day. Which day is the first on which he jumps at least 100 times in that one day? Give the day number, not the total jumps over several days.



Enter one whole number, without units.

Find the difference between two factors of 72 such that their sum is 40.

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Numbers 11, 12, 13, 14, 15 and 16 are printed on six cards. Two players pick three cards each. The sum of Player 1’s cards is 42. Player 2 has three consecutive numbers. What is the sum of the smallest and greatest numbers on Player 2’s cards?



Enter one whole number, without units.

Find the difference between the 15th and 18th terms of 44, 59, 74, 89, … . Continue the same increase between consecutive terms. Difference means the larger term minus the smaller.



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The product of $58\times24$ is

**Editorial note:** Choose one option.

What is the sum of the digits of the result of $5654+6545+5465+4556$?



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