School-Safe Puzzle Games

## School Musical Math Problem

At a school musical practice session, there are 32 tambourinists, 80 triangle beaters, 64 drummers, 112 maracas shakers, and 48 singers. The music teacher assigns the children to equal sized groups. Each group has the same number of singers, and players of each instrument.

What is the largest number of groups possible? (no student is left out)

Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!

### 18 Comments to “School Musical Math Problem”

1. RK | Founder | Profile

test

2. suineg | PUZZLE MASTER | Profile

I think the answer is 16 groups.
My reasoning was to take each number to their prime factorization, so:
2 to the 4 is the least common multiple and its 16, so 16 groups:
Each of this 16 groups would have: 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers and 3 singers.
Cool!!

3. joe | Profile

Dont know if I did this one too quickly and I am wrong but
16 groups each with
2 tambourinists, 5 triangle beaters, 4 drummers, 7 maraca shakers and 3 singers

I looked for the HIGHEST common denominator..

4. engjs1960 | Profile

16 groups of 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers. Simple factoring problem.

16 (the greatest common factor)

16 * 2 = 32
16 * 3 = 48
16 * 4 = 64
16 * 5 = 80
16 * 7 = 112

6. Mashplum | PUZZLE MASTER | Profile

16.
The GCF of all the numbers is 16. Each group has 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers.

7. Bobo The Bear | PUZZLE MASTER | Profile

There can be 16 groups (Each group has 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers).

8. suropriya | Profile

The largest number is 16

9. Hex | PUZZLE MASTER | Profile

16 groups as 16 is the greatest common divisor to 32, 48, 64, 80, and 112

10. John Lewis Highsmith | Profile

The maximum number of groups is 16 – giving 2 tambourine shakers, 5 triangle players, 4 drummers. 7 maracas shakers, and 3 singers per group.

11. Shawn | PUZZLE GRANDMASTER | Profile

Sounds like 16 groups with 21 musicians in each group.

12. cheddarmelt | Profile

16. It’s the greatest common factor.

Each group will have 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers.

13. keerthi | Profile

16 groups