As I’m sure you remember, this week’s puzzle looked like this, and you were tasked with working out what number should fill in the square with the question mark:

Solution after the break!

Okay so, the first step was to realise that you could place a number 2 on the bottom row – this will be useful. (You could also put in a 32, but since it’s in the corner it won’t help us.) So now your pyramid looks something like this:

*[EDIT: Reader Xbalanque has come up with a **better solution** than myself to solve this puzzle from here on, but feel free to follow whichever solution you prefer.]*

Truthfully, the next step requires a lot of educated guesswork.

You need to find numbers which fit the gaps in the second layer up (between 46 and 28) that add up to 30 (the number above) and the only real way to get them is by methodically trying pairs until something works. Of course, you do know that one number must be bigger than 14, and that the other is bigger than 2.

So you might start with, say, 15 and 15, but this clearly doesn’t work because 14+1 = 15 but 1+2 is definitely not equal to 15. So you can work from there. Eventually you’ll see that **21 and 9 **fit, making the middle-bottom square a 7. Now you have this:

All that’s left now is to simply work up the pyramid, filling in 67 and then, of course, **97 **in the question mark spot (those of you who guessed 67 just needed to go a little further).

See you next week for the next puzzle!

Vel.

### Like this:

Like Loading...

*Related*

March 26, 2010 at 8:56 pm

I made a little table to do the guess and check work. One row represented the ’14’ box, one row represented the ‘2’ box, and the third row represented the ’30’ location. The columns I used to pick a number for the ‘7’ box, and then I would see if the total would go to thirty. So my work looked something like this:

___|_1_|_2_|_5_|_7_|

14 | 15 | 16 | 19 | 21 |

2 | 3 | 4 | 7 | 9 |

30?| 18 | 20 | 26 | 30!|

I skipped some numbers in between when I saw the lower ones wouldn’t work. And then from there I worked up!

March 26, 2010 at 8:57 pm

Or maybe the table should look more like this…

___|_1_|_2_|_5_|_7_|

14 | 15 | 16 | 19 | 21 |

02 | 03 | 04 | 07 | 09 |

30?| 18 | 20 | 26 | 30!|

April 21, 2010 at 6:25 pm

Hey.

Bit late responding to this, some real life issues have led to me getting a bit behind my blog reading. You may recall I responded to some of your wind-up entries before. You may see a few others along the way as I continue catching up on my blog reading.

Anyway, I’d just like to point out:

guesswork is completely unnecessary to solve this puzzle. As soon as I saw you say that, I stopped reading any further in how you did your solution, because I felt like posting mine, and I didn’t have my scratch paper from while I was waiting for my sandwich when I did it the first time πGood old fashioned high school algebra is all that’s required (though most students probably don’t get reasonably good at this until they are in algebra II at the earliest).

So, let’s start with what we know, to get those two numbers below the 30.

y+z=30

2+x=z

14+x=y

y+46=w

w+30=v

v is what we really care about, the ?.

This gives us 5 equations and 5 unknowns. If we wanted to be really fancy, we’d just turn this whole thing (as in, the whole puzzle) into one big matrix thingy, and have a calculator or computer autosolve it, but let’s just do this by hand.

v=y+46+30=y+76

y+2+x=30

14+x=y

So…

14+x+2+x=2x+16=30

2x=14

x=7

y=21

v=21+76=97

So, without *any* guess work, we can find what’s in that ?.

April 21, 2010 at 9:47 pm

Hey Xbalanque!

Firstly, I’m glad you’re enjoying the puzzles, and I look forward to reading your answers to some of the others.

Secondly, thanks for taking the time to share your solution here, which is definitely superior to my own! Unfortunately when I post a solution all I’m usually posting is just the way I worked it out, since I don’t always get the answers alongside the puzzles. This means there might well be a better method, and evidently in this case there was!

Unless you object I’ll probably write up a post with your solution and include a diagram showing where each letter lies on the pyramid, so that people can see both methods π

April 22, 2010 at 2:29 am

That’s fine by me; I think a diagram will make it a fair bit clearer, and the whole point is for people to see how they can use the algebra π