Tom and Michael buy ice cream under a promotion. Tom may choose vanilla, mango, strawberry or mint. Michael may choose blueberry, Milo, chocolate or matcha. Each combination costs the amount in the table; for example, vanilla with Milo means both pay USD 3.00 for the ice cream. Which flavour should Tom choose to spend the minimum amount regardless of Michael’s choice?
Interpretation: Use the source’s intended worst-case interpretation: minimize the highest price Tom might have to pay.
Figure 1 is a stack map: each number gives the number of cubes stacked at that position. Figure 2 shows those cubes and Figure 3 shows their front view. Which option is the front view for the stack map in Figure 4?
Albert, Brad and Chris played 10 games. All three played every game, with no other participants and no ties. In each game, the winner earned 10 points, the first runner-up 4 points and the second runner-up 1 point. Albert earned 73 points and Brad 49 points in total. How many points did Chris earn?
Mary has 200 pieces of candy for 8 students standing in a straight line. Starting with student 1, she moves along the line and gives each student one piece when she stops. At student 8 she turns around and continues giving candy on the way back, repeating until all candy is gone. Which student receives the last piece?
Interpretation: A student at either end receives one piece per visit; turning around does not give that same student a second immediate piece.
In 205,000, the last three zeros are terminal zeros; the zero after the digit 2 is not. How many terminal zeros are in $1\times2\times3\times\cdots\times129\times130$?
Four boxes contain one item each: a red pencil, a green pencil, a blue pen and a black pen. Their labels say:
- Box 1: This box does not contain the red pencil.
- Box 2: The blue pen is in either Box 1 or Box 3.
- Box 3: The black pen is in Box 1.
- Box 4: This box contains the green pencil.
Boxes containing pens have true labels; boxes containing pencils have false labels. Which box contains the blue pen?
Derrick spent USD 200 in 5 days. Each day he spent no more than on the previous day, and each daily amount was an integer number of dollars. What is the smallest possible total spent on days 1, 3 and 5?
Interpretation: A daily amount may be zero; spending is nonnegative, as in the source’s example.
A very large multiple of 76 has 76 as its last two digits and has 28 positive integer factors. Express it as $n\times a^b$, where $n,a,b$ are positive integers. What is the lowest possible value of $n+a+b$?
What is the least number of whole numbers that must be selected from $\{1,2,3,\ldots,36,37\}$ to guarantee that one selected number is divisible by another?
Interpretation: Select distinct entries, without replacement. The guarantee must hold for every possible selection.
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.
In triangle $ABC$, $\angle C=120^\circ$ and $BC=2AC$. $D$ is the midpoint of $BC$, and $E$ is on side $AB$ such that $ED\perp BC$. If $BE=20$, find $AE$.
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.
