### Brain Teasers

# Alphabet Pyramids

Did you know that the mango is one of the world's most popular fruits? The mango is grown in North, South and Central America, the Caribbean, south and central Africa, as well as its native southern and south-east Asia.

The mango is also packed with vitamins A, B and C.

While eating a mango the other day, I started thinking about the ABC's. Then I remembered the set of 5-sided alphabet pyramids I had as a child.

Here are some 5-letter words that can be spelled with just 5 of my pyramids:

BELOW

CANDY

FORTY

HELIX

JABOT

LEMON

LIGHT

MANGO

OCHRE

PEACH

QUEST

QUICK

VIEUX

Using these words, can you figure out which letters appear on each pyramid?

The mango is also packed with vitamins A, B and C.

While eating a mango the other day, I started thinking about the ABC's. Then I remembered the set of 5-sided alphabet pyramids I had as a child.

Here are some 5-letter words that can be spelled with just 5 of my pyramids:

BELOW

CANDY

FORTY

HELIX

JABOT

LEMON

LIGHT

MANGO

OCHRE

PEACH

QUEST

QUICK

VIEUX

Using these words, can you figure out which letters appear on each pyramid?

### Answer

Let's start with the word MANGO, and assign a number to each pyramid.1: M

2: A

3: N

4: G

5: O

The word LEMON shares 3 letters with MANGO, so the L and E must go with the A and G, in some order. Because of the word PEACH, the E and A cannot be on the same pyramid, so the E must be on pyramid 4, while the L is on pyramid 2.

Because of the word OCHRE, neither the C or H of PEACH can be on the same pyramid with the O, so the P must be on pyramid 5.

Because of the word CANDY, the C cannot be on the same pyramid as the N, so it is with the M, leaving the H with the N. The Y cannot be with the O (FORTY), so it must be with the G, and the D is with the O. The R must then be on pyramid 2, to complete OCHRE.

1: M, C

2: A, L, R

3: N, H

4: G, E, Y

5: O, P, D

The F and T of FORTY must be on pyramids 1 and 3, but the H and T cannot be on the same pyramid (LIGHT), so the T is on pyramid 1 and the F is on pyramid 3. This means that the I must be on pyramid 5, in order to complete LIGHT.

1: M, C, T

2: A, L, R

3: N, H, F

4: G, E, Y

5: O, P, D, I

The J and B of JABOT must be on pyramids 3 and 4, but the B cannot be with the E, or else one cannot spell BELOW. Also, the W must be on pyramid 1.

1: M, C, T, W

2: A, L, R

3: N, H, F, B

4: G, E, Y, J

5: O, P, D, I

The X in HELIX must be on pyramid 1, so we now have all the letters on that pyramid. There is only one letter left on pyramid 3, and it must be in VIEUX, QUEST and QUICK, so it must be the U. The V from VIEUX must therefore be on pyramid 2.

The Q cannot be on the same pyramid as the I, in order to spell QUICK, so it is also on pyramid 2. The S cannot be on the same pyramid as the E (QUEST), so is therefore on pyramid 5, and the K is the last letter on pyramid 4.

1: M, C, T, W, X

2: A, L, R, V, Q

3: N, H, F, B, U

4: G, E, Y, J, K

5: O, P, D, I, S

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## Comments

I really enjoyed this puzzle! Just one question, where's the "Z"?

ThinksForFun, the alphabet has 26 letters. There are 5 pyramids with 5 letters each, meaning that 25 letters were used. That means one letter is left out, which is "z."

That was fun!! I didn't rate the highest difficulty because I didn't want to scare others off from trying it. Thanks so much for making it

BTW, Happy Birthday!

this teaser reminds me of these two teaser #15201 and #19621 that I submitted over 10 years ago. I like the idea of the pyramids instead of cubes though

YE! So proud of myself for getting this (though it took me a looong time lol). I finally started with the word 'mango' and it got easier from there--don't know why I didn't try that first! This was fun, and challenging (and gratifying to finally figure it out).

I used a different approach, where I built a conflict chart (a 25x25 grid with the letters across the top and down the left) to show which letters conflicted with others (either because they were in a word together, or were already known to be in a complete pyramid that didn't include the letter in question). I didn't fill in all the columns, just the ones for some of the most common letters. Then when proposing to put two letters together on a pyramid, I could run my finger down the two columns and see what other letters were compatible with both of them to see if a complete pyramid was possible that included both those letters.

I counted up the number of times each letter appeared in a word, knowing that the values of the faces of each pyramid had to add to 13 (the number of words). Then I started with the most common letters, E(7) and O(6), and tried to see what other values could fit with them.

They obviously couldn't fit together (aside from the direct conflict, they total 13 and wouldn't leave any space for the other 3 faces), and likewise none of the letters appearing 4 times could fit with E, because that would only leave a value of 2 for the remaining three faces. So the pyramid with E had to be either 7-3-1-1-1 or 7-2-2-1-1. A little experimentation showed it had to be the latter, with EGYJK the only possibilities that didn't conflict. Working with O next, it could pair with I(value 4) and then DPS were the remainig 1-value letters to make up that pyramid. Then working to see how the remaining high-value letters could fit together gave me the remaining 3 pyramids.

I counted up the number of times each letter appeared in a word, knowing that the values of the faces of each pyramid had to add to 13 (the number of words). Then I started with the most common letters, E(7) and O(6), and tried to see what other values could fit with them.

They obviously couldn't fit together (aside from the direct conflict, they total 13 and wouldn't leave any space for the other 3 faces), and likewise none of the letters appearing 4 times could fit with E, because that would only leave a value of 2 for the remaining three faces. So the pyramid with E had to be either 7-3-1-1-1 or 7-2-2-1-1. A little experimentation showed it had to be the latter, with EGYJK the only possibilities that didn't conflict. Working with O next, it could pair with I(value 4) and then DPS were the remainig 1-value letters to make up that pyramid. Then working to see how the remaining high-value letters could fit together gave me the remaining 3 pyramids.

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