# Hello can you answer my question ❔

#### Bobdahuman

##### New member
Hello humans!!
I have a question from a math comp that was in some work I did recently
If anyone has a brain much bigger than my small attempt to solve it please feel free to try it as I would really like to know how to figure it out
Thankyou
John, Chris, Anne, Holly, Mike and Nor-
man are seated around a round table, each

with a card with a number on it in front of
them. Each person can see the numbers
in front of their two neighbours, and says
the sum of these two numbers.
John says 30, Chris says 33, Anne says 32,
Holly says 38, Mike says 36 and Norman
says 41. What number does Holly have in
front of her?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello humans!!
I have a question from a math comp that was in some work I did recently
If anyone has a brain much bigger than my small attempt to solve it please feel free to try it as I would really like to know how to figure it out
Thankyou
John, Chris, Anne, Holly, Mike and Nor-
man are seated around a round table, each

with a card with a number on it in front of
them. Each person can see the numbers
in front of their two neighbours, and says
the sum of these two numbers.
John says 30, Chris says 33, Anne says 32,
Holly says 38, Mike says 36 and Norman
says 41. What number does Holly have in
front of her?

#### Otis

##### Elite Member
Hi Bobdahuman. Were you thinking with algebraic equations on paper or annotating the given sums on dadiagram?

I did both, starting with the diagram. That made it easy to see relationships.

C + N = 30

C + H = 32

N + H = 36

We could find those three unknown numbers using methods from beginning algebra. If you're more comfortable working with arithmetic than algebra, then keep notes as you ponder the relationships. For example, we can see that adding Norman's number to Chris' yields 30, but adding Holly's to Chris' instead yields 32. That means Holly's number must be 2 greater than Norman's. Also, the largest sum (36) comes from Norman and Holly, so Chris' number must be the smallest of the three (C,H,N). Thinking along these sorts of lines will allow you to guess-and-check more wisely.

If you'd like to solve the system of three equations above algebraically, experiment! (Hint: We may add and subtract equations, just like numbers.)

Maybe you'd tried something else. Please share.

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