You play the following game with a friend. You share a pile of chips, and you take turnsremoving between one and four chips from the pile. (In particular, at least one chip must beremoved on each turn.) The game ends when the last chip is removed from the pile; the onewho removes it is the loser.It is your turn, and there are 2014 chips in the pile. How many chips should you remove toguarantee that you win, assuming you then make the best moves until the game is over

Answers

Answer 1

Answer:

Each time, a person takes 1, 2, 3, or 4 chips. The strategy for a player to win the game is taking the number of chips so that the number of chips left is the form of 5k + 1 .

If It is my turn, and there are 2014 chips in the pile, I shoud take 3 chips and the left is 2011 (=5.k +1). And if the opponent takes x chips (x = 1, 2, 3, 4) , i win take 5 - x chips to guarantee the left is always in the form 5k + 1. And finally, the opponent will take the last chip.

Step-by-step explanation:

Each time, a person takes 1, 2, 3, or 4 chips. The strategy for a player to win the game is taking the number of chips so that the number of chips left is the form of 5k + 1 .

If It is my turn, and there are 2014 chips in the pile, I shoud take 3 chips and the left is 2011 (=5.k +1). And if the opponent takes x chips (x = 1, 2, 3, 4) , i win take 5 - x chips to guarantee the left is always in the form 5k + 1. And finally, the opponent will take the last chip.


Related Questions

At noon, a barista notices she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift

Answers

Answer:

She has $20 + $0.50n in her tip jar.

Step-by-step explanation:

Amount in tip jar at noon = $20

Average amount made from each customer = $0.50

Number of additional customers served after noon = n

Therefore, we have:

Additional amount made after noon = Average amount made from each customer * Number of additional customers served after noon = $0.50 * n = $0.50n

Amount in tip jar = Amount in tip jar at noon + Additional amount made after noon = $20 + $0.50n

Therefore, she has $20 + $0.50n in her tip jar.

What is the volume of the rectangular pyramid shown belown?

Answers

9514 1404 393

Answer:

  168 cubic inches

Step-by-step explanation:

The formula for the volume of a pyramid is ...

  V = (1/3)Bh

where B is the area of the base, and h is the height.

The base is a rectangle, whose are is given by the formula ...

  A = LW

  A = (8 in)(7 in) = 56 in²

Then the pyramid volume is ...

  V = (1/3)(56 in²)(9 in) = 168 in³

The volume of the pyramid is 168 cubic inches.

Which of the following proportions is true?
12 pizzas
18 people
9 pizzas
24 people
24 pizzas
48 people,
8. pizzas
20 people
20 pizzas
60 people
36 pizzas
96 people
48 pizzas
24 people
48 pizzas
60 people

Answers

12 pizzas hahaisjsjskdndhdu

determine whether or not the side lengths can be sides of a triangle 23, 16, 7

Answers

Answer:

The side lengths can not form a triangle

Step-by-step explanation:

Given

[tex]Sides: 23,16,7[/tex]

Required

Can the side lengths can form a triangle?

To do this, we apply triangle Inequality Theorem, which states that for sides a, b and c:

[tex]a + b>c[/tex]  ,  [tex]c + b>a[/tex]   and [tex]c + a>b[/tex]

In this case, we have:

[tex]23 + 16 > 7[/tex]

[tex]39 > 7[/tex] --- True

[tex]23 + 7 > 16[/tex]

[tex]30 > 16[/tex] --- True

[tex]16 + 7 > 23[/tex]

[tex]23 > 23[/tex] --- False

Hence, the side lengths can not form a triangle

4. Show that FD=1/2CB, FE - 1/2AB, and DE = 1/2AC.

Answers

can you take a picture of the problem?

TWO wires support a young tree. The wires reach the tree 2 teet above the ground
and are each 3.5 feet from the base of the tree.

Answers

Answer: 5.74 Feet Hope this helps <3

Step-by-step explanation:

A koala weighs 20 pounds. In her pouch, she carries her joey that weighs 20 ounces. What is the combined weight of the adult koala and her joey in ounces? (HELP FAST)

Answers

Answer:

kjgfdhsxfcgmnhmj,kouiyf

Step-by-step explanation:ugytfguilhyuyrtdyrjcgvh

Answer:

340 oz

Step-by-step explanation:

20 lb = 320 ounces

320 oz + 20 oz = 340 oz

Giving thanks, brainliest, or rating would be appreciated!

Javier is 1 1/2 meters tall. Which of the following is equivalent to 1 1/2 meters?
F 150 millimeters
G 1,500 millimeters
H 1,000 millimeters
J 100 millimeters

Answers

G because hehehyawgbroekenata ddndhubenesnsnd

Please help with this

Answers

Answer: 86

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

I did this before I think it was 86 not sure

In rectangle QRST, diagonals QS and RT are drawn and intersect at point P. Which of the following st
must be true?
A. AQPR must be a right triangle.
B. AQPR must be congruent to AQRS.
C. AQPR must be congruent to AQPT.
D. AQPR must be congruent to ASPT.

Answers

Answer:

C

Step-by-step explanation:

The angle QPR must be congruent to the angle SPT.

What is meant by congruent?

The congruent means the same shape and size.

Given that in a rectangle QRST, diagonals QS and RT are drawn and intersect at point P.

Since two sides are equal, it obey congruence theorem.

Consider the two congruence triangle, triangle QPR and triangle SPT.

Hence, angle QPR and angle SPT are the two congruence angle.

To learn more about congruence, use the link given below:

https://brainly.com/question/10677854

#SPJ6

Tashi Beverages Ltd. company manufacture a coca
cola juice. In a manufacturing process, 3% of tools
produced turn out to be defective. Find the
probability that in a sample of 30 tools, at most 2
will be defective?

Answers

Answer:

you spam answered my question

Step-by-step explanation:

consider this revenge

The sum of three consecutive EVEN integers is is 138. Find the smallest integer.

Answers

Step-by-step explanation:

Let x be the smallest even integer.

Then (x + 2) and (x + 4) are the other even integers.

We have x + (x + 2) + (x + 4) = 138.

=> 3x + 6 = 138

=> 3x = 132

=> x = 44.

Hence the smallest integer is 44.

Helppppp!
Regular pentagon RSTUV has sides that are half the length of regular pentagon JKLMN,
What is the ratio of the perimeter of pentagon RSTUV to the perimeter of pentagon JKLMN?
A 1:2
B, 1:4
C, 1:5
D. 1:10
E, 1:25

Answers

Answer:

A, 1:2 ratio

Explanation:

Since 1 is half of 2, and the problem states that RSTUV is half of JKLMN, A is the correct ratio.

Answer:

c

Step-by-step explanation:

17/15 - 4/5 please answer

Answers

Answer:

1/3

Step-by-step explanation:

17/15-4/5

17/15-4*3/5*3

17/15-12/15

17-12/15

5/15

1/3

The equivalent value of the fraction is A = 1/3

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p

Let the second fraction be q

Now , A = p - q

when the value of p = 17/15

And , when the value of q = 4/5

On simplifying the equation , we get

A = 17/15 - 4/5

So , the left hand side of the equation is equated to the right hand side by the value of ( 17/15 - 4/5 )

A = ( 17/15 - 4/5 )

Taking the LCM of the denominators of the fraction , we get

A = ( 17 - 12 ) / 15

On simplifying , we get

A = 5/15

A = 1/3

Therefore , the value of A = 1/3

Hence , the fraction is A = 1/3

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ6

If 1 inch on a map represents 20 miles, what is the mileage represented by 2.5 inches?
A 40 miles
B 10 miles
C 45 miles
D 50 miles

Answers

Answer:

50 miles(D)

Step-by-step explanation:

20 x 2.5

i will mark brainliest to whoever shows their work

Answers

Answer: -280000

Step-by-step explanation: Remove parentheses: (a)=a   =12x10 4  - 4x10 5

12x10 4 = 120000

4x10 5=400000

=120000-400000

then subtract the numbers:120000-400000= -280000

Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 12.

Answers

Answer:

1/36

Step-by-step explanation:

(6,6) is the only possible outcome of getting a total of 12

What is 3 3/5 x (-8 1/3)=

Answers

Answer:

Step-by-step explanation:

Convert these mixed fractions to improper fractions.

3 3/5 = 18/5

-8 1/3 = -25/3

Now, it is easier to multiply them. Multiply the numerators and the denominators.

18  x   25   =   450

5          3           15

Simplify the final answer by dividing 450 ÷ 15, which is 30.

19. Malik is 10 years less than half his mother's age. If
Malik is 12 yrs. old, how old is his mother?

Answers

Answer:

34

Step-by-step explanation:

12+12=24

24+10=34

Answer:

If he is 12 his mom would be 22.

Step-by-step explanation:

12+10=22

       </3 PureBeauty

Which statement is true about the numbers marked on this horizontal number line?

A.
0.25 -0.25
C.
-0.25 = 0.25
D.
-0.25 > 0.25

Answers

It is C because they are both equal in distance.

Answer:

B!

Step-by-step explanation:

The answer is B. id.k how to explain tho.

is the equation a true statement when x equals -3 in other words is -3 a solution to the equation 6 x + 5 = 5x +8 + 2x explained? explain

Answers

Answer: Yes

Step-by-step explanation: bc 6(-3)+5=5(-3)+8+2(-3)

Becomes -18+5=-15+8+-6 which equals -13 on both sides meaning -3 is a solution

6x+5=5x+8+2x

6x+5=(5x+2x)+(8)(Combine Like Terms)

6x+5=7x+8

6x+5=7x+8

Step 2: Subtract 7x from both sides.

6x+5−7x=7x+8−7x

−x+5=8

Step 3: Subtract 5 from both sides.

−x+5−5=8−5

−x=3

Step 4: Divide both sides by -1.

−x

−1

=

3

−1

x=−3

Answer:

x=−3

Carmelita used the multiplication table below to write ratios that are equivalent to 3/7 . One number is missing from the equivalent ratio, as shown. 21/(missing) What is the missing number?
7


9


24

49

Answers

Answer:

49

Step-by-step explanation:

Suppose that $6500 is placed in an account that pays 17% interest compounded each year. Assume that no withdrawals are made from the account.

Answers

Answer: $7,605

Step-by-step explanation:

At the end of 1 years, the amount in the account will be:

= Principal * (1 + rate)^ no. of periods

= 6,500 * (1 + 17%)

= $7,605

g Find the equation of the line passing through the point (1, 1, 1) which is perpendicular to the plane containing the points (1, 0, 0), (2, 1, 1) and (1, 1, 2).

Answers

Answer:

The equation of the line is given by:

[tex]x = 1 + t[/tex]

[tex]y = 1 - 2t[/tex]

[tex]z = 1 + t[/tex]

Step-by-step explanation:

Parametrizing the equation of the line in function of t, the equation of the line is given by:

[tex]x = x_0 + at[/tex]

[tex]y = y_0 + bt[/tex]

[tex]z = z_0 + ct[/tex]

In which we have an initial point [tex](x_0,y_0,z_0)[/tex] and [tex](a,b,c)[/tex] is a vector parallel to the line.

Line passing through the point (1, 1, 1)

This means that [tex]x_0 = y_0 = z_0 = 1[/tex]. So

[tex]x = 1 + at[/tex]

[tex]y = 1 + bt[/tex]

[tex]z = 1 + ct[/tex]

Perpendicular to the plane containing the points (1, 0, 0), (2, 1, 1) and (1, 1, 2).

From this, we get two vectors:

[tex](2-1,1-0,1-0) = (1,1,1)[/tex]

[tex](1-2,1-1,2-1) = (-1,0,1)[/tex]

The parallel vector is given by the determinant of the following matrix:

[tex]\left[\begin{array}{ccc}i&j&k\\1&1&1\\-1&0&1\end{array}\right][/tex]

Which is:

[tex]D = i*1*1 + j*1*-1 + k*1*0 - k*1*(-1) - j*1*1 -i*1*0[/tex]

[tex]D = i - j + k - j[/tex]

[tex]D = i - 2j + k[/tex]

So the vector is (1,-2,1), and the equation of the line is:

[tex]x = 1 + t[/tex]

[tex]y = 1 - 2t[/tex]

[tex]z = 1 + t[/tex]

I GIVEEEEEEEEEEEEEEEE BRAINLILSTTTT

Answers

Answer:

G

Step-by-step explanation:

brainlist

Answer: G step by step explanation:

The answer 100,400, & 600 are wrong.

2nd row 12, 20 are wrong.


Answers

Answer:

100, 400 and 1000 1st row

12, 20 in 2nd row

Step-by-step explanation:

You probably got it a wrong because in the last one 600 is not the answer the correct answer is 1000 that probably made every thing wrong

68/7 in fraction form

Answers

Answer:

9.71 in decimal form

Step-by-step explanation:

Multiply.
(4x-3)(3x+1)
Simplify your answer.
П
?

Answers

Answer:

12x^2 -5x - 3

Step-by-step explanation:

( 4x - 3)( 3x + 1  )

distribute

12x^2 + 4x - 9x - 3

combine like terms

12x^2 - 5x - 3

Hope this helps!!!

Please I need help fast

Answers

The answer is B. You divide both sides by 17pi.

Which expression has the same value as20/(10/2)

Answers

Answer:

4

tStep-by-step explanation:

do u want me to evaluate it if so the answer is 4

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