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If:
then BUCK → ?
The answer is CHICKEN.
RABBIT sounds like the noise a FROG makes, OWL sounds like the noise a WOLF makes, BEAR sounds like the noise a SHEEP makes, and MOOSE sounds like the noise a COW makes. Since BUCK sounds like the noise a CHICKEN makes, that’s the answer.
If you make a CORRECT statement, you will get either a lollipop or a chewing gum. If you make a FALSE statement, you will get either a chocolate or a car. What statement should you make in order to get the car?
You should say “I will receive a chocolate”. This statement cannot be correct, since if it was, you would get a lollipop or a chewing gum, not a chocolate. Therefore, you will get the car.
Can you find a triple of three-digit numbers that sum up to 999 and collectively contain all digits from 1 to 9 exactly once? How many such triples are there? What if the sum was 1000?
There are exactly 180 such triples that sum up to 999 and none that sum up to 1000.
In order to see that, notice that the sum of the first digits of the numbers can be no more than 9. Since the sum of all digits is 45, the sum of the middle and the sum of the last digits should be both no more than 9+8+7=24, and no less than 45-9-24=12. We then see that the sum of the last digits should be exactly 19 and the sum of the middle digits should be exactly 18. The sum of the first digits should be 45-19-18=8.
There are 2 ways to get 8 using unique digits from 1 to 9: 1+2+5 and 1+3+4.
Since the set of the first digits, the set of the middle digits, and the set of the last digits of the numbers can be permuted in 6 ways each, we get a total of 5×6×6×6=1080 solutions, or 180 up to permutation of the 3 three-digit numbers.
In order to see that we cannot get a sum of 1000, we note that since the sum of the digits from 1 to 9 is divisible by 9, then the sum of the 3 three-digit numbers should be divisible by 9 as well. Since 1000 is not divisible by 9, the statement follows.
There are N points on a circle. If we draw all the chords connecting these points and no three of them intersect at the same point, in how many parts will the interior of the circle get broken?
For example, when N is equal to 1, 2, 3, 4, and 5, we get 1, 2, 4, 8, and 16 parts respectively.
The answer, somewhat surprisingly, is not 2ᴺ⁻¹, but 1 + N(N-1)/2 + N(N-1)(N-2)(N-3)/24.
In order to see that, we start with a single sector, the interior of the circle, and keep successively drawing chords. Every time we draw a new chord, we increase the number of parts by 1 and then add 1 extra part for each intersection with previously drawn chords.
Therefore, the total number of parts at the end will be:
1 + the number of the chords + the number of the intersections of the chords
Each chord is determined by its 2 endpoints and therefore the number of chords is N(N-1)/2.
Each intersection is determined by the 4 endpoints of the two intersecting chords and therefore the number of intersections is N(N-1)(N-2)(N-3)/4!.
Below each of the following Venn diagrams there are seven tiles consisting of two letters. Place each tile in a different region so that the four tiles in each circle can be rearranged to solve the corresponding clue.
The solutions are shown below.
Which of the following is the odd one out and why?
The answer is Mars, since it spins counter-clockwise. All the other objects spin (or contain elements that spin) clockwise.
If you pull straight back on a pedal of a bicycle when it is at its lowest position, will the bicycle move forward or backward?
The surprising answer is that (usually) the bicycle will move backward.
When a bicycle moves forward, the trajectory its pedal traces with respect to the ground is called a trochoid. Depending on the selected gear of the bicycle, that trochoid could be:
Since we are fixed with respect to the ground, by pulling the pedal backward, we are causing it to move leftward along the trochoid and therefore the bicycle will be moving backward. We note that despite that, the pedal will be moving forward with respect to the bicycle (but not with respect to the ground).
You can see a visual explanation of this puzzle in the video below.
Add the 25 letters between A and Y to the grid below. Each one should appear exactly once. When you have finished, you must be able to spell the following words moving horizontally, vertically or diagonally around the grid:
AXIOM, BANQUET, CHOMP, FAWN, JOY, LURKED, RUN, STY, VYING
The solution is shown below:
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