# geometry

At Millock Highschool, there are 1,000 lockers and 1,000 students. The first day of school, all the students line up outside of the school and enter one at a time. The first student touches evry locker,the second student touches evry locker that is a multiple of two, the third student touches evry locker that is a multiple of three, the fourth student touches evry locker that is a multiple of four, and the pattern continues. when they start all the lockers are closed. read on for it to make sence.

definition:When a student touches a locker, if it is closed they open it and if it open they close it.

1.After all the students have gone, which lockers are open and which are closed?
{15points}
2. What pattern, if any, do you notice?
{5points}
3.Explainwhy these are left open.{20points}

1. 👍 0
2. 👎 0
3. 👁 925
1. http://www.braingle.com/brainteasers/teaser.php?op=2;id=7824;comm=0

1. 👍 0
2. 👎 0
👨‍🏫
bobpursley
2. There is quite a bit of documentation on this problem online. Try googling "first student touches all lockers" without the quotes. I would give you some specific websites, but I'm unable to post links. Good luck!

1. 👍 0
2. 👎 0
3. Lets look at locker number "n". All the lockers are locked to begin with. Since all the lockers are opened on the 1st pass, locker "n" is now open. For locker "n" to be closed on the 2nd pass, n must be divisible by 2. For the locker to be opened on the 3rd pass, it must be divisible by 3. For the locker to be closed on the 4th pass, it must be divisible by 4. Clearly, the locker is either opened or closed as long as the locker number is divisible by each successive divisor of "n". After the one thousandth student has made his contribution to the celebration, locker "n" will only be open if it was acted upon an odd number of times. We can therefore conclude that locker "n" will be open if, and only if, the number "n" has an odd number of factors or divisors. But the only numbers that have an odd number of factors/divisors are the perfect squares. Thus, if "n" is open, it is one of the perfect squares. The lockers that remain open are therefore numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, on up to 961.

For each locker number, find all of the exact divisors including 1 and the number itself. If the number of divisors is odd, then the number of people who reversed the locker is odd, and the locker is open. If the number of divisors is even, then the number of people who reversed the locker is even, and it is closed. The only numbers with an odd number of divisors are the perfect squares. Therefore, the lockers that remain open are those identified by the perfect squares.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math Help!

is 10 000 more than 881 462 is 1000 000 less than 2 183 486 is 1 000 000 more than 746 000 is 1 000 000 less than 624 327 207

2. ### Accounting

What is the total stockholders' equity based on the following account balances? Common Stock \$450,000 Paid-In Capital in Excess of Par 90,000 Retained Earnings 190,000 Treasury Stock 10,000 Answer A.\$740,000 B.\$730,000 C.\$720,000

3. ### maths

onvert the following to scientific notation: (i) the distance to the sun, 149 500 000 000 m (ii) the wavelength of yellow sodium light, 0.000 000 5893 m (iii) the radius of an atom, 0.000 000 000 2 m

4. ### Probability

Daily output of Marathon's Garyville, Lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. Find the probability of producing.. a. at least

1. ### Accounting

A business pays weekly salaries of \$20,000 on Friday for a five-day week ending on that day. The adjusting entry necessary at the end of the fiscal period ending on Thursday is: debit Salaries Payable, \$16,000; credit Cash,

2. ### Math

A new school has exactly 1,000 lockers and 1,000 students. the student meet outside the building and decide on this plan. The first student will enter and open al the lockers. The second student will enter and colse ever locker

3. ### math

the 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20 lockers in row. the 1 student starts with the first locker and goes down the hallways and opens all lockers. the 2 student starts

4. ### Math (Confused)

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)? a.

1. ### statistics

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least \$98,000. 112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000

2. ### Math

Newon Middle School has a hall with 500 lockers, all of which are closed. Five hundred students start down the hall. The first student opens every locker. The second student closes all the lockers that are multiples of 2. The

3. ### Trial Balance

Given the following balances, the total debits in the trial balance would equal: Equipment \$ 37,000 Accounts Payable 2,000 Sales 49,000 Accumulated Depreciation 4,000 Accounts Receivable 7,000 Retained Earnings 16,000 Salary

4. ### Accounting

O' Hara Company began operations on December 1, 2011. Presented below is selected information related to O' Hara Company at December 31, 2011. Office Equipment ₤ 40,000; Utilities Expense ₤ 6,000; Cash 14,000; Accounts