Problem Archives

17 machines, each working at the same rate, can produce 1,000 donuts in 19 days. The number of days that it would take 15 machines working at the same rate to produce 1,000 donuts can be expressed as a simplified fraction in the form a/b. What is a+b?

Answer: 338 (323/15)

Solution: June 2024 Problem Solution

Problem of February 2024

At a middle school talent show, 139 tickets were sold. Adult tickets sold for $13.50 each, and student tickets sold for $8.50 each. If ticket sales totaled $1576.50, how many adult tickets were sold?

Answer: 79

Solution: February 2024 Problem Solution

Problem of January 2024

The three-digit number ABC is 675 more than the three-digit number DEF. If the letters A through F represent distinct positive digits other than 6, 7, or 5, what is the value of ABC?

Answer: 918

Solution: January 2024 Problem Solution

Problem of December 2023

A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?

Answer: 4

Solution from the winner: A number is divisible by 15 means it is divisible by both 3 (the sum of the digits must be divisible by 3) and 5 (last digit must be either 5 or 0). We have to eliminate all the number with the last digit 0. Otherwise the first digit would be 0, which is not possible. Hence the last digit must be 5, and the number is of the form 5_5_5. There are total of 10 flippy numbers, 50505, 51515, 52525,..., 59595. Among them, 50505, 53535, 56565, and 59595 are also divisible by 3. Finally 4 five-digit flippy numbers are divisible by 15.

Problem of November 2023

A soccer ball rolls at 4 m/s towards David in a direct line from Daniel. The ball is 15 m ahead of Daniel who is chasing it at 9 m/s. At the same time, David is 30 m away from the ball and is running towards it at 8 m/s. What is the distance between Daniel and David when the ball is touched for the first time by one of them?

Daniel ball David

________________________+___________________________________

Answer: 2.5 m

Solution: The ball is rolling towards David at 4m/s and he is running towards it at 8m/s, so he gains 12 m/s on the ball. It will take him 30/12 = 2.5s to reach the ball. The ball is rolling away from Daniel at 4m/s and he is running at 9m/s, so he is gaining 5m/s on the ball. He would catch up the ball in 15/5 = 3s. Thus, David touches the ball first. After 2.5s, Daniel has gained 5x2.5 = 12.5m on the ball, so it is 15-12.5 = 2.5m from the ball when David touches it first.

Problem of September 2023

Tom enters a classroom at exactly 9:00 a.m. and notices that the 12-hour analog clock on the wall is behaving very strangely. The clock reads 4:20 and the second hand is racing very fast. In fact, the second hand makes one complete circle every 4 seconds. The minute hand and hour hand continue to behave as if every full rotation of the second hand indicates that a minute has

passed. When Tom leaves the class at 9:50 a.m., what time will the clock on the wall read?

Answer: 4:50 pm

Solution from winner:

Suppose Tom enters the classroom at 9:00 AM and leave the room at 9:50 AM. Thus, Tom was in the room for 50 minutes (not including 9 on dot) or 50 * 60 = 3000 seconds. Now, the clock read 4:20 when he enters at 9:00 AM so when he leaves at 9:50 AM, the clock should read 4:20 plus 3000 seconds (not converted). Since a full rotation occurs when 4 seconds passed, the number of minutes would be 3000/4 = 750. Divide 750 by 60 to convert it into hours (12 hours and 30 minutes). 4:20 AM will be 4:20 PM after 12 hours, adding 30 minutes to 4:20 PM yields our answer —> 4:50 PM.

Problem of August 2023

An ant walks inside a 150cm by 18cm rectangle. The ant’s path follows straight lines which always make angles of 45° to the sides of the rectangle. The ant starts from a point X on one of the shorter sides. The first time the ant reaches the opposite side, it arrives at the midpoint. What is the distance, in centimeters, from X to the nearest corner of the rectangle? (Hint: A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long.)

Answer: 3 cm

Solution from the winner:

Working backwards: The ant travels up 9 cm until it reaches the next side. Then it goes the width, 18 cm up to the next side. To dins how much cm is left when there is not enough for 18 cm (leg of the) triangles, we subtract 150 - 9 = 141 cm. Then we divide to get 141 / 18 = 7R15. The 15 cm is then traveled, and the ant is now 15 cm from one corner, but that is not the closest, so 18 cm - 15 cm equals to the answer, 3 cm.

Problem of July 2023

The cookies in a jar contain a total of 1,000 chocolate chips. All but one of these cookies contains the same number of chips; it contains one more chip than the others. The number of cookies in the jar is between one and three dozen. What is the number of cookies in the jar?

Answer: 27

Solution: July 2023 Problem Solution

Problem of June 2023

If Emily can finish a job in 3 hours, and Bob can finish the same job in 6 hours, how many minutes will it take for them to finish the job working together?

Answer: 120

Solution: June 2023 Problem Solution

Problem of May 2023

Adrian gives Bob a drawstring bag and tells him that it contains at least one chip having each of the masses 5, 11, and 19 grams. If the total mass of the chips in the bag is 56 grams, how many chips are in the bag?

Answer: 6

Solution: May 2023 Problem Solution

Problem of April 2023

What is the greatest three-digit number that is divisible by 11 and contains the digit 5 at least once?

Answer: 957

Solution: April 2023 Problem Solution

Problem of March 2023

The Staten Island Math Club is trying to schedule their in-person math club meetings for the summer 2023. One possibility is for the club to meet once per week from 3:30pm - 4:45pm. Another possibility is meeting two days per week from 3:30 - 4:40pm. A third possibility is to meet three days per week from 3:30pm - 4:30pm. The club may meet on any of the weekdays Monday through Friday during July and August. In how many different ways could the club meet?

Problem of February 2023

How many different ways are there to arrange the eleven letters in the word MISSISSIPPI? (Hint: The four S’s are identical, as are the four I’s and two P’s.)

Answer: 415 800

Solution: February 2023 Problem Solution