Snakes and ladders word problem

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Dragonkiller

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Sep 26, 2016
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Hi all,
i am new to the group and live inScotland.
My son, currently in primary education has been given a number of maths challenges and i am not sure how to advise him.
He is working on the following problem at present:

two people are playing snakes and ladders, they both throw twice and land on the same square, whcih takes them up a ladder to square 53.
They throw twice again and both land on the same square, which takes them down a snake to square 4
Each person did not throw the same number more than once. (It doesn't mention if they can both throw the same numbers)
the questions are:
a. Which number is at the foot of the ladder?
b. Which number is at the head of the snake?

could anyone give us some hints as to how we should tackle this?
thank you for any input!
 
The very first step has to be to consult with your son's instructor to determine exactly what the board of Snakes and Ladders (it's sometimes called "Chutes and Ladders" here in the United States) the problem is using. A quick Google image search revealed that there are many different variations of the board, so we definitely need to know exactly which one the instructor had in mind.
 
Hi, thank you for your replies!
A slide is commonly called a chute in Scotland, apart from in that game :D
Sorry, but there is no picture of the board and the teacher has been given the tests by an outside agency, so she doesn't know the intended board size.
i missed a vital part, that the second two throws of both people had a total which was four less than the total of the first pair of throws.
He has worked out that, since the throws must all be different number that they cant throw a double six, a one a two or a three. The fourth square had the end of the snake so couldn't be the start of a ladder.
 
Hi there,
this is the exact question. I hope this makes sense.

"Fi and Po like playing Snakes and Ladders.
In one game they noticed that after they had both thrown twice they were both at the foot of the same ladder which took them to square 53. After two more throws each, they both arrived at the head of a snake and moved down to square 4.
Each time, they threw completely different numbers. The total of the first two throws was 4 more than the total of the second two throws. Also, in the four throws, Fi did not roll the same number more than once and neither did Po.
Which numbered square was at the foot of the ladder and which square was at the top of the snake?

Thanks again for looking. ?
 
Dragonkiller said:
Hi there,
this is the exact question. I hope this makes sense.

"Fi and Po like playing Snakes and Ladders.
In one game they noticed that after they had both thrown twice they were both at the foot of the same ladder which took them to square 53. After two more throws each, they both arrived at the head of a snake and moved down to square 4.
Each time, they threw completely different numbers. The total of the first two throws was 4 more than the total of the second two throws. Also, in the four throws, Fi did not roll the same number more than once and neither did Po.
Which numbered square was at the foot of the ladder and which square was at the top of the snake?

Thanks again for looking. ?
Click to expand...

How did this go?
 
Okay, thank you for posting the full problem. Now that we have those few extra bits of information, the problem has a unique answer. The basic idea of eliminating possible die rolls based on given information is exactly how I would have approached the problem. We're told that "The total of the first two throws was 4 more than the total of the second two throws," so we know the first two throws must be at least 6. Similarly, since the first total was 4 more than the second, that means the second was 4 less than the first, so it must be 8 or less. We also know that "Fi did not roll the same number more than once and neither did Po," which eliminates several other possibilities. At this point, I'd just try a possible outcome and see if it fits with the problem. For instance:

Fi rolls a 1, and Po rolls a 5. Fi rolls a 5, and Po rolls a 1. Both are now on square 6. If we assume that's the foot of the ladder, they're now on square 53. Since the first total was 6, the second total must be 2. But the only way to get 2 is to roll 2 ones. So, then, Fi rolls a 1. Oops, Fi can't roll the same number twice. This combination fails.

Fi rolls a 1, and Po rolls a 6. Fi rolls a 6, and Po rolls a 1. Both are now on square 7. If we assume that's the foot of the ladder, they're now on square 53. Since the first total was 7, the second total must be 3. To get a total of 3, at least one of Fi's dice rolls must be a 1, but he can't roll the same number twice. This combination also fails.

Then rinse and repeat for the others. After a while, I suspect you'll start to see some patterns and eliminate multiple solutions at once, rather than having to try all of them.
 
Hi again,
thanks for the input!
we have worked our way through the combinations and still cant find just one number, but are coming up with a few options.
the first square could be 7, if the the first two throws were 4,3 the next two throws -4 could be 1,2, so the snake head would be on square 56
the first square could be 9, if the first two throws were 5,4 the next two throws -4 could be 3,2, so the snake head would be square 58
the first square could be 11, if the first two throws were 5,6 the next two throws -4 could be 3,4, so the snake head would be square 60.
We are stuck again, not sure which one it would be. Any ideas?
thank you
 
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