Lost Me Twice
Lose me once, I’ll come back stronger. Lose me twice, I’ll leave forever. What am I?
SOLUTION
The answer is TOOTH.
Category: Puzzles
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Thoka’s Rebus 3
Can you figure out which phrase is depicted by this rebus?
SOLUTION
The first image on the first row depicts a BALL. The second image depicts a BROOM which is removing the B, so you end up with BALL+ROOM=BALLROOM.
The first image on the second row depicts TOES, and the second image on the second row transforms the first letter T to a silent SH. Therefore, the final answer is BALLROOM SHOES.
Drown or Burn
The ship you are traveling on crashes and you somehow succeed to reach the shores of an island. On this island however, a cruel tribe resides and decides to murder you. The tribals can not agree on how to do this, so they decide that if the first sentence you say is a lie, they will drown you, and if it is a truth, they will burn you. Luckily, you hear their conversation and come up with a plan. What do you tell them?
SOLUTION
You can tell them “You will drown me”. This will result in a paradox – if your sentence is true, then they will drown you, but on the other hand will be forced to burn you, which is a contradiction. Similarly if your sentence if false. Therefore they will not have a choice except to give up on their plan.
The Majority Name
In a long list of names, one of the names appears more than half of the time. You will be read the names one at a time, without knowing how many they are, and without being able to write them down. If you have a very weak memory, how can you figure out which is the majority name?
SOLUTION
Remember the first name and then keep track of whether it has been repeated more than half of the time. To do that, simply add 1 if you hear the name or subtract one when you hear another name. If the list finishes and your counter is positive, then the first name is the majority. If your counter drops to 0, simply restart the procedure with the next name you hear.
This algorithm, invented by R. Boyer and J. Moore, works, because if the counter ends up at 0, then each of the names up to that moment has been read at most half of the time. Therefore, the majority name appears more than half of the time in the remainder of the list.
Under a Microscope
How much will a 12° angle measure when looked at under a microscope that magnifies 8 times?
SOLUTION
The angle will measure the same, 12°.
Word 123456789
I have a 9 letter word, 123456789.
If I lose it, I die.
If I have 234, I can 1234.
If I have 56, I am very sick.
235 is the same as 789.
What is the word?
SOLUTION
The answer is HEARTBEAT.
Ambiguous Clock
The hands of my alarm clock are indistinguishable. How many times throughout the day their positioning is such that one cannot figure out which is the hour hand, and which is the minute hand?
Remark: AM-PM is not important.
SOLUTION
Imagine that you have a third hand which moves 12 times as fast as the minute hand. Then, at any time, if the hour hand moves to the location of the minute hand, the minute hand will move to the location of the imaginary hand. Therefore, our task is to find the number of times during the day when the hour hand and the imaginary hand are on top of each other, and the minute hand is not.
Since the imaginary hand moves 144 times faster than the hour hand, the two hands are on top of each other exactly 143 times between 12AM and 12PM. Out of these 143 times, 11 times all three arrows are on top of each other. Therefore, we have 2 × (143 – 11) = 264 times when we cannot figure out the exact time during the entire 24-hour cycle.
Puzzle Giveaway 3
Our third giveaway is over. Congratulations to Steven W. who won a whole pack of socks which he plans to wear in his future Escape Room adventures.
Hey, puzzlers, our friends at Soxy are offering their comfy socks in a new puzzle pattern and want to share 5 pairs with you. Solve the puzzle below, post the answer on our Facebook wall, and you can be the lucky winner of a whole set of fun socks. Click the banner below to check Soxy’s other cool items.
Last week, I got from Soxy 1 pair of brown socks, 3 pairs of brown shoes, 2 pairs of black socks, 2 pairs of black shoes, and put them all in a wooden chest. How many times should I pick a random item from the chest, so that I end up with all-matching shoes and socks to wear on Comic-Con?
SOLUTION
You need to pick at least 14 items from the chest. If you pick 13 items, you can end up with 1 brown sock, 3 left brown shoes, 3 right brown shoes, 4 black socks, and 2 left black shoes.
Circles in the City
Get from the red square to the red circle in this intricate maze by Thomas Radclyffe.
SOLUTION
The solution is shown below.
Vectors -1, 0, 1
Consider all 1024 vectors in a 10-dimensional space with elements ±1. Show that if you change some of the elements of some of the vectors to 0, you can still choose a few vectors, such that their sum is equal to the 0-vector.
SOLUTION
Denote the 1024 vectors with ui and their transformations with f(ui). Create a graph with 1024 nodes, labeled with ui. Then, for every node ui, create a directed edge from ui to ui-2f(ui). This is a valid construction, since the vector ui-2f(ui) has elements -1, 0, and 1 only. In the resulting graph, there is a cycle:
v1 ⇾ v2 ⇾ … ⇾ vk ⇾ v1.
Now, if we pick the (transformed) vectors from this cycle, their sum is the 0-vector:
f(v1) + f(v2) + … + f(vk) = (v2 – v1)/2 + (v3 – v2)/2 + … + (v1 – vk)/2 = 0.