AMO 2027 Grades 2-3 SET 24 - Self-study

If the digits of a two-digit number are reversed to form a new number, the difference between the two numbers is 45. How many different such pairs are there?

Use the source convention: a reversed form may start with zero (for example, 04 means 4). Count each pair once, regardless of order.



Enter one whole number, without units.

If $\overline{5A8}+\overline{B2}=600$, what is the largest possible difference between digit A and digit B? The bars indicate numbers made from digits, not products. Digits range from 0 to 9; B is nonzero because B2 has two digits. Difference means the larger digit minus the smaller.

The original choices are A. 7; B. 6; C. 5; D. 3; E. 1. For this self-study edition, enter a number rather than an option letter, whether or not it appears in that list.



Enter one whole number, without units.

What is the digit in the hundreds place of $6969+9696+6996+9669$?



Choose one option.

What is the sum of the first 50 numbers of the sequence 7, 13, 27, 33, 7, 13, 27, …? Continue the repeating four-number block shown.



Enter one whole number, without units.

A rectangle is formed by placing two squares of the same size next to each other. If the perimeter of each square is 60 cm, find the area of the rectangle in square centimetres.



Choose one option.

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.

Five students entered a contest to guess the number of candies in a box. Alan guessed 25, Beth 30, Charles 27 and David 35. Roma was declared the winner. One of the four other students guessed 4 more than Roma, and another guessed 4 less. What number did Roma guess?



Enter one whole number, without units.

Rohit can go home on Diwali, which falls on Thursday, 12 November in the year described. Diwali is 45 days later. What day is today? Treat these as the calendar facts of the original question; “this year” does not mean the 2027 edition year.



Choose one option.

Fill the grid with the numbers 11 to 19, using each once, so that each row and each column sums to 45. What is X + Y?

For this self-study edition, if the stated conditions allow more than one completed grid, enter any one possible value of X + Y. No extra diagonal condition is imposed.



Enter one whole number, without units.

What number has 2 hundreds, 5 more tens than 20, and 1 less than 7? Use the source meaning: the tens contribution is 20 plus five tens, and the ones contribution is 7 minus 1.



Choose one option.

$\overline{A6B}$ is a three-digit odd multiple of 15. If its digit sum is 15, find $A\times B$. The bar denotes the number with digits A, 6, B.



Choose one option.

Calculate $76\times8+12\times8+2\times8$.



Choose one option.

What is the 11th term in the pattern 17, 20, 25, 32, 41, …? Continue the source’s intended rule: successive increases are consecutive odd numbers, beginning with 3.



Choose one option.

It takes 10 women to stitch 50 soft toys in 2 hours. How many soft toys will 6 women stitch in 4 hours, assuming all women work at the same pace?



Choose one option.

Sara’s birthday falls on Friday, 15 August this year. On which day will her birthday fall next year if next year is a leap year? Use the hypothetical year described, not the 2027 edition year.



Choose one option.