Happy New Year! Today is the first day of the Year of the Rooster, celebrated by billions of people around the world. One tradition in Chinese and Vietnamese culture is giving money in small red envelopes, usually to children. Both the money and the red color of the envelope are said to bring good luck to the child for the new year.

This year, Anh is stuffing envelopes with cash in preparation for the new year celebration; each envelope can have any amount of whole dollars ($1, $2, $3, ...) in it. She is going to give some envelopes (one or more) to her niece Mai but she's not sure how much money she wants to give yet. She wants to be prepared to give her any whole dollar amount from $1 to $14 without putting more money in or taking money out of the envelopes she has already prepared.

What is the smallest number of envelopes she has to prepare to be able to give Mai any amount in that range?

Ready for the answer?

This is a very easy question if you know a little bit about binary numbers: those 1s and 0s that fly by in sci fi movies about hackers. Those 1s and 0s represent values that are the powers of 2, and can be used to represent any whole number up to 2^{n} - 1 where *n* is the number of 1s and 0s you have.

In this case, each envelope represents a 1 or a 0. 1 represents an envelope Anh gives to Mai, and 0 represents an envelope she doesn't give to Mai.

To give Mai any whole dollar amount from $1 to $14, Anh needs to prepare 4 envelopes with the powers of 2 in them: $1, $2, $4, and $8. With those, she can actually make any amount from $1 to $(2^{4} - 1), or $15.

Astute solvers will note that because we're only trying to cover up to $14, the last envelope can have $7 in it.

This year, Anh is stuffing envelopes with cash in preparation for the new year celebration; each envelope can have any amount of whole dollars ($1, $2, $3, ...) in it. She is going to give some envelopes (one or more) to her niece Mai but she's not sure how much money she wants to give yet. She wants to be prepared to give her any whole dollar amount from $1 to $14 without putting more money in or taking money out of the envelopes she has already prepared.

What is the smallest number of envelopes she has to prepare to be able to give Mai any amount in that range?

Ready for the answer?

This is a very easy question if you know a little bit about binary numbers: those 1s and 0s that fly by in sci fi movies about hackers. Those 1s and 0s represent values that are the powers of 2, and can be used to represent any whole number up to 2

In this case, each envelope represents a 1 or a 0. 1 represents an envelope Anh gives to Mai, and 0 represents an envelope she doesn't give to Mai.

To give Mai any whole dollar amount from $1 to $14, Anh needs to prepare 4 envelopes with the powers of 2 in them: $1, $2, $4, and $8. With those, she can actually make any amount from $1 to $(2

Astute solvers will note that because we're only trying to cover up to $14, the last envelope can have $7 in it.

Happy New Year! Let's get right back into it with a teaser that lets you reuse letters. Who needs 26 different letters anyway?

There are several common English 6-letter words that use only 3 different letters. For instance, BANANA, NEEDED, MURMUR...

Can you think of a common English 7-letter word that uses only 3 different letters?

Bonus: How about an 8-letter word? (I know of at least 2 common ones.)

Ready for the answer?

Did you get it?

I know of a few common(-ish) 7-letter words:**REFEREE**, **ALFALFA**, **GINNING**, **GIGGING**, **PREPPER** (one who prepares, a survivalist).

And the 8-letter words:**ASSESSES** and **REFERRER** (something that refers you to something else).

For the HTML geeks among us, REFERRER is permanently misspelled as REFERER (note the missing R) in the HTTP specification. That's so pervasive that might even become an acceptable spelling someday.

There are several common English 6-letter words that use only 3 different letters. For instance, BANANA, NEEDED, MURMUR...

Can you think of a common English 7-letter word that uses only 3 different letters?

Bonus: How about an 8-letter word? (I know of at least 2 common ones.)

Ready for the answer?

Did you get it?

I know of a few common(-ish) 7-letter words:

And the 8-letter words:

For the HTML geeks among us, REFERRER is permanently misspelled as REFERER (note the missing R) in the HTTP specification. That's so pervasive that might even become an acceptable spelling someday.

With the new Curio Cabinet, are you *binging* on Curios? Or are you *bingeing* on Curios? Definitely, if you get too close to the fireplace, you could be *singeing* your arm hair, because *singing* your arm hair would just be weird. Either way, we know that English spelling is very challenging (or is it *challengeing*?).

Damon was bing(e)ing on Curios yesterday, learning crazy new things. When he was done, he counted the number of Curios he listened to, read, and watched. The nerd he is, he realized that the number was the smallest natural (positive, whole) number that is equal to 7 times the sum of its digits.

Nerd.

What was the number?

Ready for the answer?

We didn't say how many digits the number had, but clearly, it wasn't a single digit. So let's use our trusty friend algebra with a 2-digit number. We can write the problem out (and solve it) like this:**21 Curios** yesterday.

Damon was bing(e)ing on Curios yesterday, learning crazy new things. When he was done, he counted the number of Curios he listened to, read, and watched. The nerd he is, he realized that the number was the smallest natural (positive, whole) number that is equal to 7 times the sum of its digits.

Nerd.

What was the number?

Ready for the answer?

We didn't say how many digits the number had, but clearly, it wasn't a single digit. So let's use our trusty friend algebra with a 2-digit number. We can write the problem out (and solve it) like this:

10a + b = 7(a + b)Since we're looking for the smallest number, a = 1 so b = 2. And that means that Damon binged on

10a + b = 7a + 7b

3a = 6b

a = 2b

We founded Curious for learners like you, and we've filled it with employees who love learning, too. Some of the most mind-blowing things we've learned are bizarre facts from the animal kingdom. The *Ice Rib Toucan* mentioned below isn't a real animal, but if it were, we're sure our minds would be blown.

Take all the letters of bolded phrase below and rearrange them to form a new phrase that completes the sentence:

Where did we learn about the infamous*Ice Rib Toucan*?

In the**CURIO CABINET**, of course!

Take all the letters of bolded phrase below and rearrange them to form a new phrase that completes the sentence:

Have you heard of theReady for the answer?ICE RIB TOUCAN? It's an amazing animal, and I learned about it in the________!

Where did we learn about the infamous

In the

Had enough with the number sequences? Don't worry; I have something for those who *might* like language more than math.

I'm thinking of two words that can complete this sentence:

*In order to reach the _____, I had to _____ very carefully.*

The second word is just one additional letter added to the first word. What are the two words?

Ready for the answer?

There are actually two answers that I know of that make sense here, though I think one is a little more common.

*In order to reach the ***END**, I had to **WEND** very carefully.

Actually, there are several possible second words here that kinda work to varying degrees, like "fend", "tend", "mend", ... "Wend" makes the most sense, but who talks like that? :)

The answer I like is:

*"In order to reach the ***LIMB**, I had to **CLIMB** very carefully.

I'm thinking of two words that can complete this sentence:

The second word is just one additional letter added to the first word. What are the two words?

Ready for the answer?

There are actually two answers that I know of that make sense here, though I think one is a little more common.

Actually, there are several possible second words here that kinda work to varying degrees, like "fend", "tend", "mend", ... "Wend" makes the most sense, but who talks like that? :)

The answer I like is:

I do like me a good word puzzle. As part of the scavenger hunt that we ran a few weeks ago, I created this word puzzle because, apparently, I like torturing people. But I'm sure you guys can figure it out.

What letter(s) (the same set) can be added to the front of these words to make new words?

- _DIE
- _RAY

What letter(s) (the same set) can be added to the end of these words to make new words?

- HO_
- BELIE_
- WHERE_
- FORE_

And what do you get when you put them together?

Ready for the answer?

This wasn't the whole puzzle our team had to solve on the scavenger hunt. It was actually part of a larger puzzle.

- HOO+DIE
- HOO+RAY

- HO+VER
- BELIE+VER
- WHERE+VER
- FORE+VER

Put it together, and you get **HOOVER**.