## Interesting Words-Numbers Puzzle

Discussions on tuition centres/enrichment services that specialise in Mathematics.

### Interesting Words-Numbers Puzzle

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
BrownBelt

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### Re: Interesting Words-Numbers Puzzle

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
KiasuGrandMaster

Posts: 4673
Joined: Mon Feb 22, 2010 2:13 pm
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### Re: Interesting Words-Numbers Puzzle

Can explain the logic? thanks

cherrygal
KiasuGrandMaster

Posts: 2894
Joined: Thu Aug 06, 2009 1:01 am
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### Re: Interesting Words-Numbers Puzzle

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
BlueBelt

Posts: 391
Joined: Wed Jul 04, 2012 1:10 pm
Total Likes: 1

### Re: Interesting Words-Numbers Puzzle

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
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

Sun_2010
KiasuGrandMaster

Posts: 4673
Joined: Mon Feb 22, 2010 2:13 pm
Total Likes: 146

### Re: Interesting Words-Numbers Puzzle

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
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
BlueBelt

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### Re: Interesting Words-Numbers Puzzle

Sun_2010

Well done!

cherrygal
KiasuGrandMaster

Posts: 2894
Joined: Thu Aug 06, 2009 1:01 am
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### Re: Interesting Words-Numbers Puzzle

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.

whitecorp
BrownBelt

Posts: 575
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### Re: Interesting Words-Numbers Puzzle

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

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

Peace.

whitecorp
BrownBelt

Posts: 575
Joined: Thu Aug 11, 2011 12:38 am
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