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°.
Category: Puzzles
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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.
T and an Island
What do the letter T and an island have in common?
SOLUTION
Both of them are in the middle of waTer.
Thoka’s Rebus 2
Can you figure out which word is depicted by this rebus?
SOLUTION
The first image depicts a SEA. When you switch the third letter to C, you get SEC. The second image depicts RED. When you make the third letter a hard consonant, you get RET. The last two images depict a DIARY and DI (501 in Roman numerals). Therefore, you get:
SEC + RET + DIARY – DI = SECRETARY
Creepy Beasts Inc.
At Creepy Beasts Inc., three of the most dreaded animals, a tiger, a wolf, and a bear, sat in their boardroom in silence while they awaited their boss. Then, Mr. Tiger broke the silence.
“Isn’t it odd that our three surnames are the same as our three species, yet none of our surnames matches our own species?”
The wolf replied, “Yeah, but does anyone care?”
They sat in silence again…
Can you figure out the surname of each animal?
SOLUTION
Since the wolf replied to Mr. Tiger, his surname can be neither Tiger nor Wolf. Therefore, the wolf’s surname is Mr. Bear. Subsequently, Mr. Tiger must be a bear, and finally, Mr. Wolf must be a tiger.
Odd Rectangle
The sides of a rectangle have lengths which are odd numbers. The rectangle is split into smaller rectangles with sides which have integer lengths. Show that there is a small rectangle, such that all distances between its sides and the sides of the large rectangle have the same parity, i.e. they are all even or they are all odd.
SOLUTION
Split the large rectangle into small 1×1 squares and color it in black and white, chessboard-style, such that the four corner squares are black. Since the large rectangle has more black squares than white squares, one of the smaller rectangles also must have more black squares than white squares. Therefore, the four corners of that smaller rectangle are all black. Then, it is easy to see that all distances between its sides and the sides of the large rectangle have the same parity.
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