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Easy and True

Posted by ragknot under Tom (2 Responds)

Solve this equation …X=A*LOG(B*X+D)
A=12, B= 4, and D=7, learn the X.
It is easy and true in Excel. Type a guess of X in a cell A1, then below the guess, type … =12*Log(4*A1+7) Then copy the cell A2 to about 30 cells. An the X number will change until the X is right. It will stop changing when it can use the lots of equations.


Riddle Time (1) – I am…?

Posted by DP under SharedPuzzle, Tom, wordfun (1 Respond)

I am in the profile of some pretty great things.
If you just want to play, push me.
This is hint #3.

I am _______________ ?

Stacked Deck (part 4)

Posted by DP under Logic, Mathemagic, MathsChallenge, Tom (5 Responds)

Andy, Bob, Charlie, and Dave are ready to play another round of cards. This time it is Charlie’s turn to deal.
The cards are sorted and Charlie decides to only use the Red cards (Hearts & Diamonds).
Three [3] cards are dealt one-at-a-time to each of the four [4] players. Highest pair wins; Aces are low.
If no one wins, the cards are shuffled and re-dealt until there is a winner.

What are the odds of Charlie dealing himself a pair of 10’s AND winning?

Solution in Excel

Posted by ragknot under Tom (2 Responds)

Equation is … X=10+Log(20*X)
Loop 1 is =10+LOG(20*D4) the D4 is the guessed number above it. (Cell D4 where I guess 100)
Eash loop uses X for the number above it and before 20 loops it stops changing.
Guess a X 100 Changed =
Loop 1 13.30102999566400000000 -86.698970004336000
Loop 2 12.42491526851930000000 -0.876114727144710
Loop 3 12.39532343141620000000 -0.029591837103039
Loop 4 12.39428785897010000000 -0.001035572446172
Loop 5 12.39425157414140000000 -0.000036284828671
Loop 6 12.39425030272310000000 -0.000001271418261
Loop 7 12.39425025817260000000 -0.000000044550490
Loop 8 12.39425025661160000000 -0.000000001561048
Loop 9 12.39425025655690000000 -0.000000000054699
Loop 10 12.39425025655500000000 -0.000000000001917
Loop 11 12.39425025655490000000 -0.000000000000068
Loop 12 12.39425025655490000000 0.000000000000000
Loop 13 12.39425025655490000000 0.000000000000000
Loop 14 12.39425025655490000000 0.000000000000000
Loop 15 12.39425025655490000000 0.000000000000000
Loop 16 12.39425025655490000000 0.000000000000000
Loop 17 12.39425025655490000000 0.000000000000000
Loop 18 12.39425025655490000000 0.000000000000000
Loop 19 12.39425025655490000000 0.000000000000000
Loop 20 12.39425025655490000000 0.000000000000000

Easy and True

Posted by ragknot under Tom (7 Responds)

I did this easy and true computation about 3 years ago.
To compute X, when X is on both sides of the equation,
but one side, the X, and maybe other numbers are in a Log,
you can easily compute the X easy.

Example, find the X to several digits when X=10+Log(20*X).
Just guess an X and compute the =10+Log(20*X).
Then use the solution for the next X as a new loop.
Then if you guess the first X as 1 to 1000 the X can be
computed to many digits in about 8 loops.

So compute this X to about 10 digits.
Example: First use any number for the first X.
If you use X=1  for the first X the first loop will give 11.301029995664
If you use X=100  for the first X the first loop will give 13.301029995664
Then use the first loop X, for the next X loop.  After some loops the
X will stop changing. But if you need about 100 digits, it might take
about 30 loops


Find the missing number

Posted by Chris under Tom (7 Responds)

A Mr. Piyush has posted the following:

Find the missing number

5 : 24 :: 8 : x

Options are:
a. 65
b. 63
c. 62
d. 64

Communicating recipients

Posted by Zorglub under Tom (5 Responds)

Three recipents R(0), R(1) and R(2) each contain an integer volume v0(0) ≥ v0(1) ≥ v0(2) ≥ 1.  Each recipient is large enough to contain the combined volumes.  You are allowed to transfer some liquid from one recipient to another, only if the receiving one doubles its volume.  Show that there is always a way to empty out one recipient in finitely many steps.

Example: If the initial volumes are 17,  8,  5 the sequence of volumes could be

R(0)  R(1)  R(2)

17      8      5

17     3       10

17     6       7

17     12      1

16     12     2

14     12     4

14      8      8

14      16     0  =>  R(2) is finally empty.

Easy as 123451

Posted by Zorglub under Tom (5 Responds)

A function f takes a positive integer and returns another one by moving the leftmost digit to the right.

For example f(12345) = 23451

What is the smallest strictly positive integer n such that f(n) = 1.5 n

A yes/no test

Posted by Chris under Logic, MathsChallenge (6 Responds)

In a test involving yes/no answers, the probability that the official answer is correct is t, the probability of getting the real correct answer is b for a boy and g for a girl. If the probability that a randomly chosen boy or girl of getting the official answer to a question is 1/2, then what is the ratio of boys to girls who took the test?

It’s as easy as a, b, c

Posted by Chris under MathsChallenge (6 Responds)

Find all solutions in positive integers a, b, c to the equation
a! b! = a! + b! + c!

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