TRAININg: Third Quarter Puzzles
Chess
Level 1: Unrated-700 USCF
Black to Play and Win!
Level 2: 600-1200 USCF
Black to Play and Win!
Level 3: 1200 USCF+
White to Play and Win!
Math
Level 1:
We define nets to be flat shapes which can be folded into 3D solids. The diagram below is the net for a cube. Once folded into a cube, what number lies opposite to 2?
If you are having a hard time visualizing it, cut out a piece of paper in the shape of this net and try it out!
Level 2:
The Pythagorean Theorem was popularized by the famous mathematician Pythagoras and is used for calculating the sides of a right triangle.
When the hypotenuse (the side opposite the right angle) is labeled c, and the other two sides are labeled a and b, the Pythagorean Theorem states that a^2+b^2=c^2.
Pythagorean triples are groups of three positive integers which can form the sides of the right triangle. One example of a pythagorean triple is (8, 15, 17) since 8^2+15^2=17^2. Can you find another pythagorean triple?
Level 3:
Factorial is a special kind of notation in math that appears as an exclamation point after a number. They appear after nonnegative integer numbers and signify the product of all the numbers between 1 and the number it appears after. For example, 4!=4*3*2*1 = 24.
We can use factorials in many situations, but most commonly for counting cases. We can write the number of ways to arrange the letters M, A, T, H as 4! since there are 4 choices for the first letter, 3 choices for the second, 2 for the third, and 1 choice for the remaining letter which must go at the end.
How many ways are there to rearrange the letters F, A, C, T, O, R, I, A, L?
(Hint: There are two A’s in the set of letters we are given to work with. We cannot tell the difference between the two!)
(Bonus: What is 0! equal to? Feel free to look this one up!)
(Hint: There is one that involves numbers less than 8, 15, 17)
Archive of Our Previous Quarterly Training Puzzles
SuBMit your answers!
There's no pressure or stakes at all here - we hope that these puzzles are just a fun monthly tradition for practice! In the future, we hope to branch out to embedding interactive puzzles on this site.
As you may know, submissions to these puzzles are counted as an entry for a small raffle prize that we will distribute at our weekly workshops. Just by submitting an answer, you can earn up to two entries - one per discipline (chess/math). For each correct solution, we’ll give you another entry, for a maximum of four entries per person.
We encourage you to work on these puzzles with friends, siblings, etc. Looking forward to your answers!