Minus' Solution to

What are the odds?
Posted Weeks of January 19 - February 1, 1998

There are 36 possible combinations for a dice roll:
A1 - A6, B1 - B6, C1 - C6, D1 - D6, E1 - E6, F1 - F6

500 x 6 = 3000, so A6 is one possible combo.
1000 x 3 = 3000, so B3 is another combo.
1500 x 2 = 3000, so C2 is another combo.
3000 x 1 = 3000, so F1 is another combo.

There are 4 possible ways to roll a winner, out of 36 combinations. Thus, Catherine's odds of getting a score of 3000 in a single roll are 4/36 = 1/9.

Your Solutions

Devon Sheppard, Chris Hunter, Whitney Graham,and Kimberly Rushing, fifth-graders at South Scotland School in Laurinburg, NC, worked individually and all came up with the same tasty answer. Here's how they did it:

They multiplied 6 by 6 to get 36 possible outcomes.  Some of the students actually worked up a chart to see what the possible outcomes would look like.  They then discovered that the ways that 3000 could be reached are:
A(500) and 6
B(1000) and 3
C(1500) and 2
F(3000) and 1
These make for four possible ways.

They then turned these numbers into a fraction 4/36; so the odds are 4 out of 36. 

Cameron Sexton, Austin Dyches, Ashley Carter, Nicholas Bradley, T.L. Driggers, Jessi Barnes, and Kathryn Rogers, also of South Scotland School in Laurinburg, NC, worked out the same odds as their classmates above, but they went one-step further to make it even yummier for Minus
They went a step further and reduced the fraction (4/36), ending up with 1/9, or the odds being 1 out of 9.

Jeremy Cole, a grade 7 student in Patricia Fields' class at Robert Smalls Middle School in Beaufort , SC, must have been cooking up a storm in the kitchen. His delightful and well-explained solution sent Minus' tastebuds on a mini-tour of the heavens.
The answer to the dice problem is 1/9 for the following reason: If Catherine has to get a score of 3000, she needs to find out how many ways she can get 3000 out of  possibilities. She can get 3000 four ways. So, there are four out of thirty-six or one out of nine ways That Catherine can get  3000.

Ng Kam Kiew, in Malaysia, impressed Minus with a little South East Asian cuisine. Take a look at Kam Kiew's spicy concoction.
There are 36 combinations of the two dices thrown (6 for the first multiplied by 6 for the second.) There are only four possibilities that the total will be 3000. They are:

A6 (500 X 6 = 3000)
B3 (1000 X 3 = 3000)
C2 (1500 X 2 = 3000)
F1 (3000 X 1 = 3000)

So, there are only 4 possibilities out of 36 or 1 out of 9. The odds are 1 out of 9. Or 1 for and 8 against.

Kwok Wah [kwokwah@cadvision.com] provides yet another way to make this dish a gourmet dream. Notice how this visionary chef worked solely in fractions. Scrumptious!
She has 1/36 chance to get A and 6, 1/36 chance to get B and 3, 1/36 chance to get C and 2, and 1/36 chance to get F and 1.

Therefore it comes to 1/36 + 1/36 + 1/36 + 1/36 = 1/9
The chance to score 3000 is 1/9.

We only have an e-mail address for this mystery chef [GTsang@ibm.net], but Minus still wanted to thank him or her for "playing with the odds".
First of all, find out how many possibilities can make 3000 with both of the dice.  A with 6, B with 3, C with 2 and F with 1.  Then find out how many possibilities there are out of everything, A with 1, A with 2, A with 3 etc.... 

It turns out to be 4 possibilities to get 3000 and 36 combinations for all the numbers.  So she has 4 out of 36 chances to get 3000, or 1 out of 9 chances.

Nathan Perkins of Corrales, NM, and Dave McChesney [dmcchesney@pierz.k12.mn.us] both fed Minus a tid-bit for dessert. Here it is, but don't blink--you may miss it! ;)

If Minus had arms, he would
hug you all. Thanks for this
week's feeding frenzy.
See you back here soon!