The worlds first riddle!

H/T
a) >+1T P(E)=3/4
b) =2H P(E)=1/4
c) +1T1H P(E)=1/2

Neighbors kids
a) 2G1B P(E)=3/8
b) >+1B P(E)=7/8
c) 2B1G|1G P(E)=1/4
b) 2B1G|1B P(E)=1/2

If not applause then prayer

Rap

Try:
Since when is 19 a digit?

WHIM'S PROBLEM

Rap:
I don't think reusing a number is allowed. Otherwise, you could pick 1 and generate all positive integers.

Whim:
I'm confident 17 is the max. It can be done with these combinations:
2, 3, 10
2, 3, 14
2, 6, 11
2, 6, 13

I guess I don't understand the problem

But is my 'whim' to play with triangular numbers
Tri# E {1,3,6,10,15,.......,T(n-1)+n} so the counting numbers become
1=1
2=3-1
3=3
4=3+1
5=6-1
6=6
7=1+6
8=6+3-1
9=6+3
10=10
11=10+1
12=10+3-1
13=10+3
14=10+3+1
15=15
16=15+1
17=15+3-2
18=15+3
19=15+3+1
20=15+6-1
21=21
and so on

Rap

Thanks Mark for confirming 17 is max. I was not sure. I found 2, 6, 11 and 2, 6, 13.

whim

Rap,

If you want to express all positive integers in terms of triangular numbers, why not do it the easy way?

n = T(n) - T(n-1)

Whim,

I tested all combinations up to 200, that's why I'm confident.

Of course, it does
By Induction

T(0)=0
T(1)=1
& 1=.T(1)-T(0)
& n=T(n)-T(n-1)
if true then
n+1=T(n)-T(n-1)+1
now show that
n+1=T(n+1)-T(n)

if so, then
T(n)-T(n-1)+1= T(n+1)-T(n)
T(n+1)= 2T(n)-T(n-1)+1
T(n+1)= T(n)+[T(n)-T(n-1)]+1
T(n+1)=T(n)+n+1
&
n+1=T(n+1)-T(n)
so if holds for all n
QED

Markr, another example where you've shown me why my forehead is sloped.

Rap

I don't think so (forehead).

Actually, n = T(n) - T(n-1) is derived directly from the definition you gave: T(n) = T(n-1) + n.

Try:
Here's the second solution to
WHIM+TRY+TRY=AGAIN
if you want it:

8625+749+749=10123

A favorite alphametric of mine

in prose it is "all Eve overdid was talk talk talk."

as a relation

EVE/DID=.TALKTALKTALKTALK........

Rap

Mark the wise wrote, "Since when is 19 a digit?"


The term "digit" is often used to represent a number in a specific position in a larger number.

Anywho, no such restrictions were placed on the solution. I remain confident that any compassionate, kind and generous sole would, in all fairness allow the result to stand. Are you such a person?

I wrote this before you posted the answer, which I will not look at until I have this thing beat.



Rap, or was it Rap: (The one with the less than vertical cranial profile)


H/T
a) >+1T P(E)=3/4
b) =2H P(E)=1/4
c) +1T1H P(E)=1/2

Neighbors kids
a) 2G1B P(E)=3/8
b) >+1B P(E)=7/8
c) 2B1G|1G P(E)=1/4
b) 2B1G|1B P(E)=1/2

"If not applause then prayer."


Given the choice…Applause it is.


I know the answer to the TALK/TALK so I won't spoil it for others. However if you have a spare, two minutes try:





Want to work in a Library?

(Please read the question carefully, as failure may disappoint)



How many unique ways can one arrange 4 books out of 10 on a shelf



How many unique ways can you arrange 5 books on a shelf



How many unique ways can one arrange 6 books on a shelf



What are the number of ways of arranging 8 different books on a shelf if they can be arranged in any order




Happy 4th July to you all (and the Brits) without whom there would be no party.

BOOKS 4/10
The question seems a bit ambiguous. I'll assume you're asking how many ways 4 books can be arranged within 10 possible positions.
10!/(10-4)! = 5040

BOOKS 5
5! = 120

BOOKS 6
6! = 720

BOOKS 8
8! = 40,320

EVE DID TALK was done on April 7/8 of this year.

1+2+2+3+3=11

Mark:
171219

WHIM=1307
MARK=7842

Rap

Mark:

BOOKS 4/10
The question seems a bit ambiguous. I'll assume you're asking how many ways 4 books can be arranged within 10 possible positions.
10!/(10-4)! = 5040

You assume correctly!

BOOKS 5
5! = 120

BOOKS 6
6! = 720

BOOKS 8
8! = 40,320

Great stuff




Rap:

WHIM=1307
MARK=7842




:wink:




How many ways can you choose 3 numbers from 10 when order doesn't matter


Two dice are rolled. What is the probability that neither die shows a 6



Two dice are rolled. What is the probability that at least one die shows a 6


What is the probability of getting the following sums on the roll of two fair dice:

(a) 4



(b) 8





Alive without breath,
As cold as death;
Never thirsty, ever drinking,
All in mail never clinking.

I am


The more you take, the more you leave behind.

I am


'Twas in heaven pronounced, and 'twas muttered in hell,
An echo caught faintly the sound as it fell;
On the confines of earth 'twas permitted to rest,
And the depths of the ocean its presence confessed;
'Twill be found in the sphere when 'tis riven asunder,
Be seen in the lightning and heard in the thunder.

'Twas allotted to man with his earliest breath,
Attends him at birth, and awaits him in death,
Presides o'er his happiness, honor, and health,
Is the prop of his house, and the end of his wealth.
In the heaps of the miser 'tis hoarded with care,
But is sure to be lost on the prodigal heir.

It begins every hope, every wish it must bound,
With the husbandman toils, and with monarchs is crowned.
Without it the soldier, the seaman may roam,
But woe to the wretch who expels it from home!
In the whispers of conscience its voice will be found,
Nor e'en in the whirlwind of passion be drowned.

'Twill not soften the heart; but though deaf be the ear,
It will make it acutely and instantly hear.
Yet in shade let it rest, like a delicate flower,
Ah... breathe on it softly, - it dies in an hour.

I am


h i j k l m n o
What word does this represent

'Twas in heaven pronounced, and 'twas muttered in hell, ...
Ah... breathe on it softly, - it dies in an hour.

I am

the letter h

h i j k l m n o
What word does this represent

water

C(10,3)
120

NO SIX
25/36

AT LEAST 1 SIX
11/36

FOUR
1/12

EIGHT
5/36

I KNEW IT WASN'T A KEEPER
2 + 1609 + 23 + 98763 + 8 = 100405

72
35+2=37 (35+37=72)
37-2=35 (37+35=72)
24*2=48 (24+48=72)
48/2=24 (48+24=72)

2-DIGIT NUMBER
48

OXFORD
d = 5000*sqrt(h) (all in meters)

SIX+SIX+SEVEN=TWENTY
650 + 68782 + 68782 = 138214