Interesting Words-Numbers Puzzle

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Interesting Words-Numbers Puzzle

Postby whitecorp » Mon Aug 26, 2013 11:55 pm

Received this query on my AllExperts page and sharing it here:

Hello,
My math teacher gave us a worksheet with six 4-letter words.
Book = 13
Full= 19
Sail= 20
Boil = 11
Silk = 18
Foil = 10
Each letter in the word has a value and they all should equal the number after the word.
also, the B for instance in the word Book has to be the same value as the B in the word Boil, and etc.
I cannot figure this out after hours of trying. How do I do this? Thank you for your time!



Peace.

whitecorp
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Re: Interesting Words-Numbers Puzzle

Postby Sun_2010 » Tue Aug 27, 2013 12:26 pm

whitecorp wrote:Received this query on my AllExperts page and sharing it here:

Hello,
My math teacher gave us a worksheet with six 4-letter words.
Book = 13
Full= 19
Sail= 20
Boil = 11
Silk = 18
Foil = 10
Each letter in the word has a value and they all should equal the number after the word.
also, the B for instance in the word Book has to be the same value as the B in the word Boil, and etc.
I cannot figure this out after hours of trying. How do I do this? Thank you for your time!



Peace.


1=O
2=L
3=I
4=F
5=B
6=K
7=S
8=A
9=U

Sun_2010
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Re: Interesting Words-Numbers Puzzle

Postby cherrygal » Tue Aug 27, 2013 12:55 pm

Can explain the logic? thanks

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Re: Interesting Words-Numbers Puzzle

Postby XXXX » Tue Aug 27, 2013 12:59 pm

Sun_2010 wrote:
whitecorp wrote:Received this query on my AllExperts page and sharing it here:

Hello,
My math teacher gave us a worksheet with six 4-letter words.
Book = 13
Full= 19
Sail= 20
Boil = 11
Silk = 18
Foil = 10
Each letter in the word has a value and they all should equal the number after the word.
also, the B for instance in the word Book has to be the same value as the B in the word Boil, and etc.
I cannot figure this out after hours of trying. How do I do this? Thank you for your time!



Peace.


1=O
2=L
3=I
4=F
5=B
6=K
7=S
8=A
9=U


FULL is meant to add to 19 but your solution gives 17.

Presumably there's a typo in the question, which unfortunately likely makes it impossible to solve...

What was your method? Intuit that O,I,L must be 1,2,3 in some order and try out permutations?

XXXX
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Re: Interesting Words-Numbers Puzzle

Postby Sun_2010 » Tue Aug 27, 2013 2:05 pm

XXXX wrote:.



FULL is meant to add to 19 but your solution gives 17.

Presumably there's a typo in the question, which unfortunately likely makes it impossible to solve...

What was your method? Intuit that O,I,L must be 1,2,3 in some order and try out permutations?



No typo, my mistake :oops:
It should be L= 3 and I =2


1+2+3+4=10
Since foil =10 , they must be 1,2,3,4

Boil=11
So b=f+1
So f must be 4 , b must be 5

Book=13
ook=13-5=8
So o has to be 1 and k is 6

From sail and silk, a= k+2=8
Sail=20.
i+l=5 so s =7

So u can only be 9

From full =19, L= 3 and I=2

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Re: Interesting Words-Numbers Puzzle

Postby XXXX » Tue Aug 27, 2013 4:04 pm

Sun_2010 wrote:
XXXX wrote:.



FULL is meant to add to 19 but your solution gives 17.

Presumably there's a typo in the question, which unfortunately likely makes it impossible to solve...

What was your method? Intuit that O,I,L must be 1,2,3 in some order and try out permutations?



No typo, my mistake :oops:
It should be L= 3 and I =2


1+2+3+4=10
Since foil =10 , they must be 1,2,3,4

Boil=11
So b=f+1
So f must be 4 , b must be 5

Book=13
ook=13-5=8
So o has to be 1 and k is 6

From sail and silk, a= k+2=8
Sail=20.
i+l=5 so s =7

So u can only be 9

From full =19, L= 3 and I=2


Nicely done. I was blinded by trying to keep the letters in alphabetical order for some reason.

XXXX
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Re: Interesting Words-Numbers Puzzle

Postby cherrygal » Tue Aug 27, 2013 4:36 pm

:thankyou: Sun_2010

Well done!

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Re: Interesting Words-Numbers Puzzle

Postby whitecorp » Tue Aug 27, 2013 8:16 pm

When I solved this for the student, I took into account the possibility that the value assigned to each letter may not be unique (the problem certainly doesn't emphasize it must be for that matter).

In such circumstances a myriad of answers can be obtained. One logical set would be:

A=9, B= 2, F=1, I=1, K=7 , L=6 , O=2, S=4 and U=6.

And many more can be computed.

Peace.

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Re: Interesting Words-Numbers Puzzle

Postby whitecorp » Thu Aug 29, 2013 7:07 pm

For those who are interested, I have answered things here on my site:

http://www.a-levelmaths.com/apps/blog/s ... er-problem

Peace.

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