Math Is Fun Forum

Hi Median Joe,

I'm confused. Did you deliberately omit the brackets?

Anyway, if (M−A) weren't subtracted, M & A's ages would be identical at that point (which they're not). Mary's age at that point is stated by the 'bright spark' as being (3/2)(M−k).

I used the same method: see post #4's "Note: Their age difference at each stage is a constant, which in the first stage is established as being 2c (ie, 3c - c)."

Hi Median Joe;

Yes, I also got the answer 27.5.

I'd forgotten about the algebraic method I showed in these two threads I opened back in 2009 - Rita's age & Edna's age - and instead went straight to Excel's Goal Seek to solve your puzzle.

Below is my solution to your puzzle, adapting the algebraic method I posted here:
============================================================
Let c = Ann's age when Mary was 3 times as old as Ann.           

Note: Their age difference at each stage is a constant, which in the first stage is established as being 2c (ie, 3c - c).       

                                           Mary    Ann	
when Mary was 3 times as old as Ann was      3c      c	
when Ann is 3 times as old as Mary was              9c	
when Mary was half as old as Ann will be   4.5c   2.5c	
Mary is twice as old as Ann was              5c     3c

So Mary's present age is 5c and Ann's is 3c, from which 5c + 3c = 44 (their given combined present age).           
           
Solving: c = 5.5           
           
∴ Mary is 27.5 (5*c = 5*5.5) & Ann is 16.5 (3*c = 3*5.5).
============================================================
The following equation is based on the above info, and evaluates to c = 5.5:

I haven't looked at your solution yet, nor your "Not quite sure why you subtract M - A?" question, but I will...

Hi Bob & CurlyBracket;

I solved it this way:

A = B^2 - 108
B = A^2 - 158

Solution 1:
    Substituting B into the first equation resulted in A^4 - 316A^2 - A + 24856 = 0 ... which I couldn't solve longhand, only online (eg, WolframAlpha) or with CAS (eg, Mathematica, Excel).
    Answer: A = 13

Solution 2:
    Trial & error: Evaluating the first 2 equations with A = 13 yields B = 11, evaluating with B = 11 yields A = 13, and figures in either direction from those yield increasingly large errors.
    Answer: A = 13

Hi CurlyBracket;

Yes, that's my reasoning also (see post #2), and my m=RIGHT((2016-ax-by)/3+x+y) expression is an attempt to state it algebraically.

I probably cheated by employing spreadsheet's RIGHT function to extract the last digit of 708, but used that to keep the expression small (though non-standard).

Hi CurlyBracket;

Nice one!

I hope I got it right!

Edit 5/5/2022: Improved my solution (see post #4)

Q : Qajaq (Inuit) n a kayak
Q : Qulliq (Inuit) n a type of oil lamp used by Inuit people

Both are valid Scrabble words: Scrabble™ Official Word Check

That link is to the Collins online Scrabble word checker that uses the official tournament word list, including over a quarter of a million permissible words. It's endorsed by Mattel and the World English-Language Scrabble™ Players’ Association.

MIF has a 'full precision' calculator here, that gives the 'full precision' answer 0.9999999999999071250152, which is accurate to the 22 decimal places present in the sum.

Hi Bob;

I found the following solution ranges (in ascending 7-digit permutation order):
  (a) 720 solutions for sums of 3 single-digit numbers and 2 double-digit numbers, ranging from 1+2+4+36+57=100 to 7+6+4+52+31=100
  (b) 288 solutions for sums of 1 single-digit number and 3 double-digit numbers, ranging from 2+15+36+47=100 to 7+56+24+13=100

Hi ganesh;

Hi Bob,

Just playing with Excel's Solver (not that kumark23's puzzle needs that sort of help), and it found your solution.

There's also another solution (the one I found manually just before my first post) that the Solver doesn't find without me first entering something somewhere on the grid...and I stumbled across several options of what to put where to extract that solution.

One Solver shortcoming is that it stops computing at the first solution it finds, but sometimes I've managed to get more than just the one result by influencing Solver's computation process somehow...eg, as per the above.

Hi kumark23, and welcome to the forum;

This type of puzzle usually lists the numbers that you have to choose from to fill the blank squares, and each number can only be used once.

Those numbers are often 1 to 9, and this group solves your puzzle.

Hint: The top row can only contain a particular group of three numbers that sum to 24.

Hi jabah013.307,

Here's the image: