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Question 4: Give me five

Three dice are rolled. What is the probability that the numbers showing total 5?

Answer: Well done to all who rolled in with 2.78% (or similar): Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Hans-Bernd Luechtefeld, consultant, Germany; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Tom Jenkins????, business development, R.D. Abbott Co., Inc., Garden Grove, California, USA; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and everyone else who had a go.

SOLUTIONS

Amparo Botella

Each die has 6 faces, so when rolling three dice:

6×6×6=216 

Thus, the total number of possible outcomes is 216.

We need to find all sets of three numbers (from 1 to 6) whose sum is 5:

(1,1,3)(1,3,1)(3,1,1)(1,2,2)(2,1,2)(2,2,1)

Since these are all distinct orders, we count 6 valid cases.

The probability is given by dividing the number of favorable cases by the total number of cases:

6/216=1/36≈0.0278

The probability that the sum of the three dice is 5 is 1/36 or approximately 2.78%.

John Bowen

The ways of getting 5 are 6: 1,2,2/2,1,2/2,2,1/3,1,1/1,3,1/1,1,3 whereas there are 6 x 6 x 6 = 216 possible outcomes from rolling 3 dice,

So, the probability of getting 5 is 6/216 = .0,02777 or 2.8%

Kamila Staszewska

Rolling 3 dice gives 6*6*6=216 possibilities in total.

All combinations that sum to total 5:

1+1+3, 1+2+2, 1+3+1+, 2+1+2+, 2+2+1, 3+1+1 (6 outcomes)

Probability of dice showing total 5 is 6/216 = 1:36 (2.78%)

Hans-Bernd Luechtefeld

If you roll three dices, you can achieve a total of 5 in the following way:

1 1 3

1 3 1

3 1 1

1 2 2

2 1 2

2 2 1

And that's it. Only 6 possibilities.

The total number of ways to roll three dice is

6x6x6 = 216

The probability of getting a total of 5 is 6/216 resp. 1/36 (or ~2,78%).

Sudi Sudarshan

A sum of 5 with three dice can be obtained with the following permutations:

1,1,3; 1,3,1; 3,1,1

1,2,2; 2,1,2; 2,2,1

The probabilities are each (1/6)(1/6)(1/6) = 1/216

There are 6 ways that give us the desired outcome.

So, the combined probability = 6*(1/216) = 1/36

Tom Jenkins

Rolling 3 dice, there are 216 potential outcomes (63)

Of the potential outcomes, there are 6 that total 5

Therefore the probability is 6/216 = 1/36 = 2.7…%

Andrew Knox

Each dice thrown has a 1/6 chance of landing on a specific number. To have the 1st, 2nd and 3rd dice all fall on 1, the chance is 1/6 x 1/6 x 1/6 = 1/216.

There are more permutations possible if the numbers are to add up to 5 (6 permutations):

1   2   2

2   1   2

2   2   1

1   1   3

1   3   1

3   1   1

So the chance of adding up to 5 becomes a factor 6 higher, i.e. 6/216.

 

New teaser on Monday.

1/1 = O, 2/2 = W, 3/3 = R, 4/4 = ?

Answer: R. Well done to: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; John Bowen, consultant, Bromsgrove, UK; David Mann, polymer business development consultant, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands;

SOLUTION

As so neatly described by Amparo Botella (and others):

1/1 is the first letter of word One

2/2 is the second letter of word Two

3/3 is the third letter of word Three

4/4 is the four letter of word Four

New teaser on Monday

 January 1st, 1901; February 4th, 1908; March 9th, 1927;  ?

Answer: This one was all about seeing the squares and cubes in the dates, as neatly worked out by: David Mann, Polymer Business Development consultant, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Saurav Dey, senior engineer, technical support division, Mitsui Chemicals Singapore R&D Centre, Pte. Ltd, Singapore Science Park II, Singapore; Tom Jenkins???, business development, RD Abbott Co. Inc., Garden Grove, California, USA; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA. Well done also to Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain, for his interesting, alternative take on this question.

SOLUTIONS                                                                                                  

David Mann

Of the dates are expressed as month / day / year then the numbers are the original number followed by its square and cube.

We have

1/1/1

2/4/8

3/9/27

So the next will be 4/16/64 ie 4th April 1964.

Kamila Staszewska

Good morning,

The date is the following:

Month – is the next month which is April (4)

Day – is a square of the month (4*4=16)

Year is month and day multiplied 4*16=64

The date is April 16th, 1964

Andrew Knox

Answer: 16th April 1964.

Pattern appears to be month x day = last two digitale of the year. Months are in a sequence of Jan thru’ December and days follow a sequence of 1, 4, 9, (delta is = 3, 5, 7, 9, 11) so next date will be 16th April 1964.

John Bowen

Good morning Patrick,

Next date is April 16th 1964

In each given case, the day is the square of the month, and the last two digits of the year are the product of the day and month. The progression is 1, 1x1 =1, +1900 = 1901, so 1st January 1901

then 2, 2x2 + 4, 2x4 +8, so February 4th 1908

then 3, 3x3 = 9, so March 9th 1927

so 4, 4x4 = 16 so April 16th 1964

Saurav Dey

Answer: April 16th, 1964

Date: Formulaà Date/month/19(Date*month)

1/1/1901à 22/2/1908à 32/3/1927à 42/4/1964

Sudi Sudarshan

The dates when expressed in numerical fomat of m/d/yy are:

1/1/01, 2/4/08 and 3/9/27 . These are in the form d/d^2/d^3 beginning with 1.

So, the next date would be 4/4^2/4^3 or 4/16/64.

Since the other dates are in the 20th century,  the next date is: April 16, 1964

Amparo Botella

I think the next date is April 16th. 1958

The month is the next one – Jan. Feb. Mar. April.

The day has an increase of an odd number 1+3=4 + 5= 9 + 7= 16

The year is an increase of 7 (+12)= 19 (+12)= 31 what means 1901 +7= 1908 + 19= 1927 + 31 = 1958.

Tom Jenkins

What number comes next in this series?

318, 342, 366, 474, 586, ?,...

Answer: This time it's hats off to Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland, the only reader to resolve this most tricky teaser:

Digits of the number multiplied + the number = next number

3*1*8+318=342

3*4*2+342=366

3*6*6+366=474

4*7*4+474=586

5*8*6*+586=826 is the answer.