hifadhinitz
2022-09-04
Answered

How many squares of all sizes arise using an 𝑛-by-𝑛 checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length 𝑛 ?

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Sarahi Gallegos

Answered 2022-09-05
Author has **4** answers

It is very simple to see how many 1-squares fit. What about a 2-square (natural notation)? Well, let's only place the top-left square. How many places can we put the top-left square of a 2 by 2 on the board and have it fit? And so on? This leads to your intuition being correct.

asked 2021-09-09

In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?

asked 2021-09-08

A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?

asked 2022-09-29

Find the shortest sequence of numbers between 1 and K (K=99) such that each pair of numbers are adjacent somewhere in the sequence (1231 is an answer if K=3).

asked 2022-06-19

If there are 20 people with 17 men and 3 women and they seat themselves randomly at 4 Tables (A,B,C,D) with 5 people each. With all arrangements being equally likely, what is the probability that no woman sits at table A ?

asked 2022-09-17

The non-iterative method for calculating graycode depends on Log2N bytes, to store position information for the next bit in the iteration sequence.

Specifically, the goal is to know the next bit to change without having to look at the current code.However, for the 3 bit gray code, there's a iteration sequence 0,1,2,1,0,1,2,1 that can be represented with a much simpler function - maintain "0,1,2,1" in a register and rotate each time (as an example of a more general permutation).To reduce the necessary state, this could be kept in two positions, starting 0,1 and a constant function of "xor, permute" applied: 0,3 => 1,0 => 2,1 => 3,2 => 0,3 (the bit to change being the first, and 3 handled as 1 since only 0,1,2 are valid)

Is it possible for graycodes to exist for higher values of N, such that the iteration function can be calculated with just a permutation operation?

Specifically, the goal is to know the next bit to change without having to look at the current code.However, for the 3 bit gray code, there's a iteration sequence 0,1,2,1,0,1,2,1 that can be represented with a much simpler function - maintain "0,1,2,1" in a register and rotate each time (as an example of a more general permutation).To reduce the necessary state, this could be kept in two positions, starting 0,1 and a constant function of "xor, permute" applied: 0,3 => 1,0 => 2,1 => 3,2 => 0,3 (the bit to change being the first, and 3 handled as 1 since only 0,1,2 are valid)

Is it possible for graycodes to exist for higher values of N, such that the iteration function can be calculated with just a permutation operation?

asked 2022-05-28

There are 4 rows and 3 columns in a table, and each slot is painted with black or white with equal probability, and I wish to find the probability that one, and only one of the rows is painted black. What I did was:

$P=4\cdot (1/2{)}^{3}\ast (7/8{)}^{3}=\frac{343}{1024}$

and it indeed seems to be the correct answer. I thought I should also try solving it using combinatorics, but that is something I fail to do. My try is:

$\frac{4\cdot 1\cdot ({2}^{9}-7)}{{2}^{12}}=\frac{505}{1024}\ne \frac{343}{1024}$

what have I done wrong?

$P=4\cdot (1/2{)}^{3}\ast (7/8{)}^{3}=\frac{343}{1024}$

and it indeed seems to be the correct answer. I thought I should also try solving it using combinatorics, but that is something I fail to do. My try is:

$\frac{4\cdot 1\cdot ({2}^{9}-7)}{{2}^{12}}=\frac{505}{1024}\ne \frac{343}{1024}$

what have I done wrong?

asked 2022-07-16

How many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1