Show Digest for last: 2 Days | 3 Days | 5 Days | 1 Week | 2 Weeks

Six words are to be entered, one across each row of the grid.

The colors are present to create individual regions. In each region all the letters are the same. Two adjacent regions have different letters; non-adjacent regions may or may not have the same letter regardless of same or different color.

Clues for the words in the four middle rows (rows 2-5), in random order, are:

• hot dog topping
• VCR's "go back to start" button
• negligent
• language of Warsaw

---

From Mensa Puzzle Calendar 2019 by Fraser Simpson, Workman Publishing, New York. Puzzle for June 14.

Take a 7x7 grid of squares and remove the center square.

Take two 5x5 grids of squares and remove each center square.

Cut the smaller figures into as few pieces as possible and reassemble to form the larger.

Is it possible to use fewer pieces if you are allowed to remove a different square than the center any of the original shapes?

Lucy stands on a set of faulty scales that state her mass as 48 kg. David's mass from the same scales is recorded as 56 kg and their combined mass is recorded as 107 kg.

Assuming the magnitude and nature of the errors was constant, what is the true mass of David?

Given that 13⁴-6⁵+5⁹ is the product of exactly 5 distinct prime factors, what is the largest?

Let f:ℝ→ℝ be twice differentiable such that f(0)=2, f'(0)=-2, f(1)=1

Find for at-least how many c ∈ (0, 1)

f(c).f'(c)+f''(c)=0

is satisfied.

There are two identical uniform spherical planets of radius R. The first has its center at the origin of the xyz coordinate system. The second has its center at (2R, 0, 0). The planets are touching.

A projectile is launched from the "North Pole" of the first planet at (0, 0, R) with its initial velocity pointed in the direction of the vector (1, 0, 1).

Let the escape speed relative to the planet's surface be v_e. Note that here, the escape escape is for a single planet in isolation (following the typical convention).

With the given launch vector, let v₀ be the minimum launch speed for the projectile to reach the "North Pole" of the second planet at (2R, 0, R).

How are the two speeds v_e and v₀ related?

If cos x is irrational, find maximum positive integer n such that cos 2x, cos 3x, ... cos nx are all rational.

If 3n zeros are placed between the digits 3 and 7, then the number formed is divisible by 37. In addition, if 3n+1 zeros are placed between the digits 7 and 3, the number formed is also divisible by 37.

It means 3000...7 is divisible by 37. Here,the zeroes are in 3n form.

It means 70000...3 is also divisible by 73. Here zeroes are in 3n+1 form.

Prove it.

A: Why are obtuse angles always so 123425521?
Q: Because they are never 46789!

In the above joke recover the coded words.

All nerds are smart. Some teachers are nerds. Some teachers are fake smart. Some geeks are gamers. Some geeks are smart. Some gamers are dumb. Some gamers are teachers. If we split the geeks evenly between types of geeks what is the fraction of smart geeks.

We have a series where the sum of any 7 consecutive terms is negative and the sum of any 11 consecutive terms is positive. What is the maximum number of terms in this series?

A, B, C, and D are four positive integers whose sum is 2019. What are the largest and smallest values that A*B+B*C+C*D can be?

There are two vertical poles, one of height 100 feet and the other 70 feet, positioned a horizontal distance of 80 feet apart on level ground. A rope of length 100 feet connects the tops of the two poles. A weight, placed on the rope so that it can slide freely along it, is allowed to come to rest.

Find the horizontal distance of the weight from the 100 feet pole and the vertical distance from the ground.

Seven balls of different weights are randomly painted red, orange, yellow, green, blue, indigo and violet, each ball being painted a distinct color.

The green ball is found to be heavier than the blue ball, and the red ball is found to be heavier than the yellow ball.

What is the probability that the red ball is heavier than the blue ball?