Puzzle

Find the hidden flag.

Solution

Send me your solution at contact@adamgluck.com!

Part 1

You bought 12 special dimes at a yard sale. After getting them inspected by your local numismatist, he determines one is a counterfeit due to it being slightly heavier than the others.

Once you get home, you find out that you've mixed up the coins. All you have to determine which coin is counterfeit is a balance scale.

What is the least number of weighs you can use to determine which coin is counterfeit?

Part 2

Suppose you don't know whether the counterfeit coin is heavier or lighter than the other coins.

How can you determine which coin is counterfeit and whether it's heavier or lighter than the real coins using only 3 weighs?

Solution

Send me an email at contact@adamgluck.com!

Credit

Steven J. Miller

Problem

You have 8 pirates friends who jointly find a giant treasure chest. Since they don't trust each other, they decide to secure the chest by locking it with $n$ distinct locks and have you distribute keys among them such that:

• Any group of 5 or more pirates can unlock the chest
• Any group of 4 or fewer pirates cannot unlock the chest

What is the minimum number of locks you need, and how many keys will each pirate receive?

Clarifications

How many locks can a specific key unlock?

Each key can unlock exactly 1 lock. However, there can be any number of duplicates for each key.

How many keys can be given to each pirate?

You can give each pirate up to the $n$ keys, where $n$ is the number of locks there are.

Solution

Send me an email at contact@adamgluck.com!

Credit

Steven J. Miller

Part 1

You are a spy tracking the richest man in New York and snap a picture of a page of his diary. However, it appears to be encrypted with some sort of cipher. The text is below:

grhakcl iqozel go vctckwakl dck kvr pagrl opl doklp go vctckwak
grgbeg gqpcrgpal eabogz gbegvvcqbpl kavaosgiza dczzct hvgzzobm
hgxakl bgsomgpobm hckpgzl gbe auavqpobm baup ialp gvpocbl kasabqa
vxvza pagrl qla grhakcl pc auhgbe vghgvopx vqp gscoegiza eabogzl
gbe gvvazakgpa vglf topfcqp geeobm fagevcqbp grhakcl ol vqkkabpzx
vczzavpobm gicqp cba rozzocb vzgorl gbe aomfp fqbekae rozzocb ob
kasabqa dck opl vqlpcrakl

What was the man writing about?

Part 2

Your next mission is to spy on the top chef of New York to figure out his secret ingredient. You find an envelope with the below text:

LARNILRVWAAWECKRPULERRHAPGRONNRAEMIOCMNINBAHOLERNIRBBOYHCVLHEBENOLEC
UEENMWSEIVTERVSATAOHHTAIEDSLCOYSETEERCFIWYAXMPITSRDTHBPSAASMHBNLAEIC
HAEVNGXETDAOAYDAPEEUKEOAAEEEDSMIRYSSROATFXNOINAEMRSKCIEELEDSTSUNPADU
JJATNRSTSESSHSSENRCEOAMRUITMAEEIWLSDLIOIEBOAHCROIEOLLEAOGIONTAANEIYJ
OOUCTLNFEFIDTNCTRIYTESHPLHUVMLEETCLLANRHDFDULCTFCCUUITOELDONLNEYSEHA
PSESIQEOKLEEIDNUULNMOROIOYCNITLEYEAIDTSEMEWCNOKYDFANMHATTCYNEBTNEDNE
YSEWBRERTHITAAVAALKPOHBORIOSVBPEUNGPGCHYEBDYEUJSFPYYGDTTEFCRLKERSHIN
CTRDOIRTAAVPEICFTTWTSURVITAACBTRL

What does the envelope say?

Part 3

Your last mission is to decipher the lab notes of a evil scientist. You find this text file on a thumb drive by his computer:

15122122231111342112445351231114325342255234434212114451433351124141
34423311124233531233233123213433422331324351234451232121344233254341
44112334312312215534521525111251345214124231445123253421344342345234
21245334115243421232435342311252344342433241125215234112523425121125
43422523445221124231234144151221341323213441415352122434113452142152
51434233521444344233124231111213142354121153125234434252153421412312
42214451433351124121125123254341444321233143323253422552344342215215
12525251124221324351413112521255345215435352213431232332322325522111
23123134423352432112322351124231414351234451233134255212241123254331
23151221222311113421433252234253212331344212251231234134255123212312
51251512423134423153215251342321521512525123455334512315343315512311
34122434113452142153251512213234421242252343512543414434112351215515
34112334522512422423251512111123423334423352431123125142345221231123
33124225231242312344512321213454234443552351411222233452242311435423
31241444514333511241412351215515432342354314251123124212242152511225
523443422112423125434225342123214311535234434221

What were his notes about?

Solution

Send me an email at contact@adamgluck.com! Also send an email if you would like a followup post with harder ciphers.¹

Problem

You're making a pea casserole for your friends and bought 9 cans of 100 normal peas. Your friend Benjamin is a picky eater, so you buy an extra can of 100 special peas to make him a special dish. Each normal pea weighs 1.0 gram, while each special pea weighs 0.9 grams.

Before you start cooking the casserole, you realize you've mixed up the cans! The cans are all open (but not mixed together yet) and you have a disposable electronic scale that can be used exactly once to find the weight (in grams) of any number of peas from any number of cans.

How can you find out which can has the special peas?

Solution

Send me an email at contact@adamgluck.com!

Credit

Steven J. Miller

Problem

You are trying to send your brother in Australia a bag of gold coins. You both have a unique lock and key set, along with access to the UPS (the United Pirate Service) to deliver the coins. The UPS will safely deliver your packages, but they will steal anything that is in an unlocked package. You can send packages back and forth to your brother through the UPS as many times as you want.

How can you send the coins to your brother without them being stolen by the pirates?

Clarifications

Can my key unlock both locks?

No, each key only works with the original lock in its set. You and your brother each start with a different lock and key set.

Can I send my key through the UPS?

Yes, but it will get stolen unless it is in a locked package. You should assume anything sent that is not in a locked package will be stolen.

How do I lock the package?

You can use any type of box or container for your package so the choice is yours!

Solution

Send me an email at contact@adamgluck.com!

Credit

Steven J. Miller

Problem

You find yourself trapped in a dark cave with a box of matches and two sticks. Each stick will take exactly 60 minutes to fully burn when one end is lit. However, the sticks burn at irregular rates (one half might burn in 50 minutes while the other half burns in 10 minutes).

How can you use these supplies to measure 45 minutes?

Solution

Send me an email at contact@adamgluck.com!

Problem

You recently adopted a pet elephant and noticed he's been stomping nonstop since arriving at your house.

After careful observation, you discover he's creating an infinitely long sequence made up of two distinct stomps: right foot stomps and left foot stomps.

In any given position of the sequence, the probability of the stomp being a right foot stomp is $p$ (where $0 < p < 1$), while the probability of a left foot stomp is $1-p$.

How can you use this random sequence of stomps to derive the value of $\pi$?

Solution

Send me an email at contact@adamgluck.com!

Part 1

You are a king hosting a grand party. To accommodate your guests, you order 1000 barrels of your most expensive wine. A day before your party, your trusted advisor tells you exactly one of the barrels has been spiked with Gluvenom: a deadly poison that kills its victims in exactly 24 hours no matter the dosage.

Luckily, you have a dungeon full of prisoners. There is just enough time for a wine tasting trial where you can assign a set of barrel(s) to your prisoners and have them taste a drop of each. If a prisoner drinks from the poisoned barrel, they will die before the party with enough time for you to identify and destroy the toxic barrel.

What is the minimum number of prisoners you need for the trial to deduce which barrel was poisoned?

Clarifications

Can you have 1000 prisoners each taste a different barrel?

Yes. If you label the barrels 1 to 1000 and assign a prisoner to each barrel, whichever prisoner dies will indicate which barrel number is poisonous. However there are ways to solve this using a smaller number of prisoners.

Can you use the order/timing of when the prisoners taste the wine in the solution?

No. All prisoners must taste their assigned barrels simultaneously, and all results (deaths) occur at the same time. You cannot use the order or timing of events to solve the problem.

Part 2

After the smashing success of your first party, you decide to host a second celebration with another 1000 barrels of wine. Your advisor warns you that once again, exactly one barrel has been poisoned with Gluvenom.

However, this time you have 48 hours to identify the toxic barrel (instead of 24 hours like in Part 1).

Since the poison takes exactly 24 hours to take effect, you can now conduct two sequential wine trials:

1. First trial (Day 1): Assign each prisoner a specific set of barrels to taste from, just like in Part 1
2. Second trial (Day 2): After 24 hours, any prisoners who survived the first trial can taste from a different set of barrels

What is the minimum number of prisoners you need to find the poisoned barrel?

Part 3

You decide to have a final party with your last 1000 barrels of wine. Predictably, you find exactly one barrel has been poisoned with Gluvenom yet again. However, this time you only have 20 prisoners remaining in your dungeon after the events of your first two parties. Feeling guilty, you want to ensure as many prisoners survive the wine trial as possible.

After a single trial, what is the maximum number of prisoners you can guarantee the survival of while still finding the poisoned barrel?

How about with only 10 prisoners left?

Solution

Send me an email at contact@adamgluck.com!

Problem

There are 900 elephants in a race. Bob and Charlie know which elephants are in 1st and 2nd place.

You are allowed to ask Bob a question about the race that he will respond to with a number from 1 to $n$. After that Charlie will give you the number of either the 1st or 2nd place elephant.

You have to use Bob's answer to determine whether Charlie's number is the 1st or 2nd place elephant.

What is the lowest upper bound of $n$ Bob can give you so that you can determine if the elephant Charlie gave you finished in 1st or 2nd?

Clarifications

Can you ask Bob which elephant got first place?

Yes, if you ask Bob who got first place, you can use his answer to determine whether the elephant Charlie gives placed 1st or 2nd. However the upper bound for $n$ in this case is 900 (there are better answers).

Can Bob answer with fractions or decimals?

No, he must either answer with whole numbers or have the ability to map his possible answers to whole numbers.

Can you ask Bob multiple questions?

You can make the question you ask Bob as long as you want. However, Bob is only allowed to answer with a single number. You are allowed to make each digit depend on a sub-question, but then the lowest upper bound would be the range of possibilities that Bob would answer with.

For example, you could ask Bob 2 yes or no questions and have him answer with a 2 digit number (1 digit per question) where 1 means yes and 2 means no. Since there would be 4 possible answers Bob could give (11,12,21,22), the upper bound for $n$ would be 4.

This Sounds Like a Math Problem?

What problem isn't a math problem! Here's a version of the riddle formatted as a math question:

• Let $A$ = The set of answers Bob can give
• Let $E$ = The set of unique elephants in the race
• Let $\mathcal{F} = \{f : E \times E \times A \to \{0,1\}\}$ be the set of questions you can ask Bob where:
  • $f(\text{🐘}_a, \text{🐘}_b, \text{ans}) = 1$ if elephants $\text{🐘}_a$ and $\text{🐘}_b$ can be distinguished using Bob's answer $\text{ans}$
  • $f(\text{🐘}_a, \text{🐘}_b, \text{ans}) = 0$ otherwise

Find the minimum possible $|A|$ such that:

Solution

Read my writeup or send me an email at contact@adamgluck.com!