Ã山ǿ¼é

The Challenge 24 Competition is a mathematics competition for 3rd-, 4th-, 5th-, 6th-, and 7th-graders, hosted each spring by the Ã山ǿ¼é Department of Mathematics. Participants play the , which involves a deck of cards, each showing four whole numbers between 1 and 9. When presented with a card, the players strive to be the first to combine the four numbers to make 24 using only addition, subtraction, multiplication, or division. Many cards have more than one solution. The game can be surprisingly challenging, but the participants in Challenge 24 are quite good, having previously won competitions within their own schools.

The co-coordinators of the Challenge 24 Competition are Ms. Angela Castle and Dr. Christine Uhl.

The 24 Game

The 24 Game was developed in 1988 by Robert Sun to provide students with a fun way to discover patterns among numbers. Sun founded the company Suntex International Inc. to market the game.

Each card in the 24 Game is marked with one dot, two dots, or three dots to indicate its level of difficulty. Generally, the higher the number of dots, the more challenging the card.

To the right is a two-dot card containing the numbers 2, 3, 4, and 4. Try making 24 with the numbers on this card. Remember: you must use each of the numbers 2, 3, 4, and 4 exactly once and the only operations you may use are addition, subtraction, multiplication, and division. (Since you must use each of the numbers 2, 3, 4, and 4 exactly once, you will end up using 4 twice.) You may use an operation more than once. There are three essentially different solutions for this card. Can you find all of them?

To Ã山ǿ¼é Students: Help!

The Department of Mathematics needs about 30 volunteers to run the Challenge 24 Competition. If you would like to work with kids who love math, sign up to help us! Elementary education majors are particularly encouraged to volunteer. The competition is held on a Saturday in March or early April. The next competition will be planned in the fall, at which time volunteers will be solicited by email and in mathematics classes.

The 2024 Challenge 24 Competition

The 2024 Challenge 24 Competition was held on Saturday, April 13. Over 60 students from seven area schools participated this year. The participating schools were Allegany-Limestone Middle School, Hinsdale Central School, Olean Intermediate-Middle School, East View Elementary (Olean), Salamanca, Washington West Elementary (Olean), and Bysiek CPA Homeschool.

Medals and $1000 scholarships to St. Ã山ǿ¼é were awarded to the first, second, and third place students in each grade. Congratulations to all!

Third grade

• First place: Jack Crawford (Washington West)
• Second place: Nilaa Saravanan (Washington West)
• Third place: Mason Smith (Washington West)

Fourth Grade

• First place: Anvitha Balineni (Olean Intermediate Middle School)
• Second place: Irene Yang (Olean Intermediate Middle School)
• Third place: Jacob Moses (Hinsdale Central School)

Fifth Grade

• First place: Aadhav Rajaramanathan (Olean Intermediate Middle School)
• Second place: Kavya Saravanan  (Olean Intermediate Middle School)
• Third place: Aisha Aylin (Olean Intermediate Middle School)

Sixth Grade

• First place: Grant Perry (Olean Intermediate Middle School)
• Second place: Elan Thach (Olean Intermediate Middle School)
• Third place: Owen Talbot (Olean Intermediate Middle School)

Seventh Grade

• First place: Mia Jones (Olean Intermediate Middle School)
• Second place: Jenna Goodling (Hinsdale Central School)
• Third place: Abigail Simons (Olean Intermediate Middle School)

Inside a Challenge 24 Competition

On a cold Saturday morning in March, you might expect elementary school and middle school students to be watching TV, texting their friends, or playing outside among the remnants of winter. You may be mostly right---but not completely. In western New York, some 3rd-, 4th-, 5th-, 6th-, and 7th-graders have traveled with parents and teachers to St. Ã山ǿ¼é to compete in a math competition. That's a rather beautiful thing.

The Challenge 24 Competition is organized by Ms. Angela Colomaio, Dr. Christine Uhl, and about five Bona's students. The organizers are aided by about 30 volunteers, who range from Ã山ǿ¼é students to Ã山ǿ¼é faculty to middle school teachers to parents. The organizers and volunteers are here for one reason: to celebrate the wonderfully-talented elementary and middle school students who love math so much that they spend a Saturday morning in a math competition. Challenge 24 also celebrates the teachers and the parents who coached and supported their students and children.

Individual Round: During the Individual Round, students compete against the deck and the clock. As this round progresses, the room is is suffused with the murmur of arithmetic operations. The proctors are amazed by the mathematical skills demonstrated by the participants in Challenge 24.

The Individual Round requires a large number of proctors; some parents and teachers lend a hand to help the round proceed more efficiently. Thank you!

Group Round: During the Group Round, students within each grade level compete against one another in groups of four.

Group Finals: Challenge 24 culminates with the Group Finals, in which the top six students from each grade level compete against one another. Rather than solve a single card, students must now supply a missing number to solve two cards simultaneously.

Award Ceremony: Medals, in the traditional colors of gold, silver, and bronze, and $1000 scholarships to St. Ã山ǿ¼é are presented to the first, second, and third place students in each grade level. Subsequently, photos of the winners are printed in the Olean Times Herald.

Fantastic Facts about the 24 Game's Magic Number

•  The most challenging Challenge 24   There are many sets of four numbers between 1 and 9 that cannot be "solved" in accordance with the rules of the 24 Game. The set {1, 1, 1, 1} isn't solvable, for example, because the numbers are too small to reach 24 using the four operations of arithmetic. Of course, 24 Game cards show only solvable sets of four numbers. However, there are some solvable sets of numbers that do not appear on any 24 Game card. The two most challenging solvable sets for the 24 Game are {3, 3, 7, 7} and {3, 3, 8, 8}. Can you make 24 from these sets following the rules of the 24 Game?

•  Divide and conquer   24 has eight positive divisors: 1, 2, 3, 4, 6, 8, 12, and 24. That's a lot of divisors for a small number. This may be why Robert Sun chose 24 as the "target" number for his game. The more divisors a number has, the easier it is to make the number from a product of two numbers. There are four products that equal 24: 1x24, 2x12, 3x8, and 4x6. The lowest integer possessing more divisors than 24 is 36.

•  Just the factorials, ma'am   24 is 4 factorial, written 4!. The factorial of a positive integer n is the product of the integers from 1 up to n. Thus, 4! = 1x2x3x4 = 24. Factorials are fantastically useful in the theory of counting. For example, suppose you're holding four 24 Game cards. The number of ways you can can order the cards from first to fourth is 4! = 24.

•  More fun factorials   24 factorial, written 24!, equals 620448401733239439360000, which has precisely 24 digits. The only other positive whole numbers n for which n! has exactly n digits are 1, 22, and 23.

•  One day at a time   There are 24 hours in a day---a fact that allowed "24" to be the title of a popular TV series. The 24-hour day seems to have originated with the ancient Egyptians. The Egyptians liked counting in base 12, perhaps because the human hand has 12 finger joints. (A hand has four fingers and a thumb; each finger has three joints.) With one hand, you can use your thumb to count to 12 on your finger joints. (Try it and see.) Base-12 seems rather odd to us, but is it really any stranger to use a base-12 number system because a hand has 12 finger joints than it is to use a base-10 system because two hands have 10 fingers (well, eight fingers and two thumbs)? Given their affection for base-12, it was natural for the Egyptians to divide the day into 12 parts and the night into 12 parts, which led to the modern 24-hour day.

•  It's worth a shot   The NBA uses a 24-second shot clock to time possessions by the offensive team. The shot clock was invented by Danny Biasone, the late owner of the Syracuse Nationals, in the 1950s to try to speed up the game and prevent teams from stalling. Why 24 seconds? Biasone figured that the average number of shots two teams would take during a game was 120. He divided that number into the length of a game, which is 48 minutes or 2,880 seconds. The result is 2880/120 = 24 seconds.

•  Far side of the Moon   To date, exactly 24 human beings have travelled to the Moon. "Travelled to" means "reached Moon orbit or landed on the Moon". Of these 24, 12 walked on the Moon. Thus far, all manned missions to the Moon occurred between 1968 and 1972.

•  License to derive   You can play the 24 Game using New York license plates! The license plates for most NY cars have the format LLL-DDDD, where L is a letter and D is a digit between 0 and 9. The four digits can, in principle, be used for the 24 Game. However, unlike the 24 Game cards, some license plates have one or more zeroes and it's not always possible to make 24 from the digits on a license plate. Nevertheless, the game can be successfully played with the license plates of many---perhaps most---NY cars. Speaking of cars...

•  A good sign   The Interstate 86 exit closest to St. Ã山ǿ¼é is Exit 24.