AMO 2019 Primary 6 (Grade 6)

Find the sum of the digits of $93517+35179+51793+17935+79351$.

How many four-digit numbers have a digit sum of 5?

Four darts are thrown at the dartboard shown. A miss scores 0. Add the four scores. What is the least whole-number score that is impossible to obtain?

The ages of three brothers sum to 32. The oldest is twice as old as the youngest. The two older brothers differ in age by 3 years. How old is the youngest?

A locker combination has five different digits. The second is twice the first; the third is 50% more than the second; the fourth is 1 more than the first; the fifth is 2 more than the fourth. Find the sum of the digits.

A method squares numbers ending in 5: $25^2=625$ uses $2(2+1)=6$ followed by 25; $35^2=1225$ uses $3(3+1)=12$ followed by 25; $45^2=2025$ uses $4(4+1)=20$ followed by 25. If $245\times245=100N+25$, find $N$.

Jessica folds a paper rectangle in half to form another rectangle, then folds it in half again to form a 6 cm by 6 cm square. What was the area of the original rectangle, in square centimetres?

All 600 people going to an event are in couples. A couple cannot be split between buses, and each bus holds at most 65 people. What is the least number of buses needed if every bus carries the same number of couples?

How many three-digit whole numbers have digits in strictly decreasing order from left to right?

In $\overline{AB}\times\overline{BA}=\overline{A45B}$, $A,B$ are different digits; both factors have two digits and the product has four digits. If $\overline{AB}<\overline{BA}$, find $\overline{BA}$.

The cards shown fold along their dotted lines so that each shows either its number or its letter. Chrissy sees all six cards. The visible numbers sum to 11. How many different sets of visible numbers are possible?

Find the ones digit of $2^{10}+3^9$.

Triangle $CAB$ has area $27\text{ cm}^2$. Find the total area of its two unshaded triangles, in square centimetres. The small grid squares are equal.

All six faces of the cube shown are painted black. It is cut into 64 identical smaller cubes. How many small cubes have paint on at least two faces?

The five-digit number $\overline{4A12B}$ is divisible by 99. How many possible values can it have?

An M-shaped MOEMS-tile is a 5 by 5 square with two 4 by 1 rectangles removed, as shown. What is the maximum number of tiles Jimmy can place on a 6 by 42 board without overlap? Tiles may be turned over or rotated as in the source construction.

How many digits are in the second-smallest positive multiple of 41 that consists only of digit 1?

The octagon shown is the union of two overlapping squares, whose overlap is also a square. The larger square has side 6 cm. The smaller has side 4 cm and one corner at the centre of the larger square. Find the area, in square centimetres, of the smallest square that can surround the octagon.

A football league has 10 teams. Each team plays exactly 3 games against every other team. How many games are played in total?

One light flashes every 7 minutes and another every 2 minutes. Both flash at 1 PM. How many minutes after 3 PM do they next flash together?