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You have two solid cubes of lead, which have almost the same size. You cut a hole in one of them and pass the other one through it. After measuring the cubes later, it turns out that the larger cube is still heavier than the smaller one. How is this possible?
You cut a hole in the SMALLER cube, and pass the larger cube through it. “Prince Rupert’s cube” is the largest cube which can pass through a unit cube, and it is approximately 6% larger.
Can you help square find his way back to his friends? On the way, look out for:
The solution is shown below.
First, get a completely untangled rope. Now, your task is to grab its two ends, and without letting it go, tie this knot in the middle.
In order to do this, first cross your arms, and from this position, grab the two ends of the rope. Once you untangle your arms, the knot will appear on the rope.
Can you see which letters are connected with each other in this 3D maze?
The solution is shown below.
When you have me, you want to share me.
When you share me, you no longer have me.
The answer is SECRET.
Is it possible to design a simple closed curve inside a box, such that its projections on all 6 walls of the box are trees, i.e. curves without loops?
Yes, it is possible, as shown on the image below.
Huey has 3 donuts, Dewey has 5 donuts. Louie comes along and the three of them split the donuts equally. In exchange, Louie offers 8 candies to Huey and Dewey. What is the fair way to split the candies?
Huey must take 1 chocolate, and Dewey must take 7. This is because each of them ate 8/3 donuts, and therefore Huey gave away 1/3 of a donut, whereas Dewey gave away 7/3 of a donut.
You throw away the outside and cook the inside. Then you eat the outside and throw away the inside. What do you eat?
The answer is CORN.
What two animals do these sums spell?
PANTS + TRAP – STRAP + HERD + APPLE – DAPPLE = PANTHER
HIP + POP + EAR – PEAR + POTATO + EMU – TOE + SCOT – COT = HIPPOPOTAMUS
None of these statements is correct.
At most 1 of these statements is correct.
At most 2 of these statements are correct.
…
At most 98 of these statements are correct.
At most 99 of these statements are correct.
How many of these statements are correct?
If the number of true statements is X, then statements 1, 2, … , X are wrong, and the rest are correct. Therefore X = 100 – X and X = 50. Thus, there are 50 correct statements.
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