The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Trying to Solve a Challenging Number Puzzle

Date: 07/28/2006 at 13:10:02
From: James
Subject: Advice on lateral thinking to answer a number puzzle?

Add the numbers: 

4 + 3 x 2 =
6 - 5 =     

Wrong answers I've come up with include 1, 2, 6, 7, 8, 10, 14, 15, 20,
25, 29, 31, 33, 34, 43, 44, 45, 49, 53, 54, 63, 73, 82, 87, 88, 117
and so on.

I have calculated every possible number combination, as you can see
from the wrong answers.  Those combinations have and haven't included
the missing answers to the sums. I just need to know how to interpret
"Add the numbers".

A general thought process is obviously incorrect as all possible
logical answers are wrong.  The answer needs a lateral thought process
so I need guidance on how to achieve this.

Date: 07/28/2006 at 14:51:28
From: Doctor Ian
Subject: Re: Advice on lateral thinking to answer a number puzzle?

Hi James,

We get questions like this a lot, and our suggestion is always the
same:  Spend your time on something more productive, because there
isn't a correct answer. 

Here's an analogy.  Suppose I tell you I'm thinking of a color, and
you want to guess it.  If I'm thinking of "blue", and you guess
"blue", I can just change my mind to make you wrong.  And there is an
effectively infinite range of colors that I can think of, so I never
have to admit that you're right, no matter how many guesses you make. 

As far as we can tell, that's exactly what's going on with this kind
of puzzle.  There are infinitely many ways that you might come up with
an answer.  For example, have you considered that

  - letters like M, I and V are also Roman numerals, as are
    combinations like IV and MI? 

  - that each letter (and digit) has an associated ASCII value, 
    and an EBCDIC value, and each letter has a positional value 
    within the alphabet, and that lowercase and uppercase letters
    can be treated as distinct or as equivalent? 

  - that "e" is a common abbreviation for the base of the natural
    logarithm, 2.72828...? 

  - that "i" is a name for the imaginary unit, defined such 
    that i^2 = -1?  

  - that the "nine" in "nineteen" might also be considered 
    "one of the numbers"? 

  - that "the numbers" might include all the numbers that you can
    form from the components that you're given (e.g., that 6 and 
    5 can be combined to make 56 and 65, and that the letters "T",
    "E", and "N" can be combined to make "TEN")? 

  - that "add" might refer to string concatenation, rather than
    an arithmetic process?

  - that "add" might refer to modular arithmetic (e.g., 11 o'clock
    plus 4 hours equals 3 o'clock)?

  - that I could keep going like this forever?  

What this means is that the person asking it can just say that any
answer you come up with is "wrong".  

Or, to put that another way, _any_ answer you come up with is correct
if you've got a reasonable explanation for it, so you can stop as soon
as you find one you like.  And if the person asking the question says
that he's got a different one in mind, you can reply that if he wants
to specify a unique answer, he's got to be less ambiguous about how he
words the question. 

- Doctor Ian, The Math Forum 
Associated Topics:
High School Puzzles

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.