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Consider the integer powers of 7: a(n) = 7^n:
7, 49, 343, 2401, 16807,... 117649, ...

Prove that the second from right digit in all those numbers (excluding the 1st) is either 0 or 4.

(No Solution Yet, 1 Comments) Submitted on 2018-12-16 by Ady TZIDON    

Three concentric circles each have radii 8, 15 and 17.

Find the largest possible area of the equilateral triangle with one vertex on each circle.
(No Solution Yet, 2 Comments) Submitted on 2018-12-15 by Danish Ahmed Khan    

Begin with a finite sequence of blocks in a row, each in one of 3 colors: red, blue, yellow.

Below each pair of neighboring blocks place a new block with the color rule: If the blocks are the same color use that color but if they are different use the third color.

Example:

r b y y b
 y r y r
  b b b
   b b
    b
How can the color of the last block be easily predicted from the top row?

Note: I don't know the full answer but can solve special cases.

(No Solution Yet, 4 Comments) Submitted on 2018-12-14 by Jer    

Difficulty: 3 of 5 Discs in Triangle (in Geometry) Rating: 3.00
Find the side length of the smallest equilateral triangle in which three discs of radii of 2, 3, 4 can be placed without overlap.
(No Solution Yet, 2 Comments) Submitted on 2018-12-13 by Danish Ahmed Khan    

What is the highest prime number with no repeated digits?

(Solution Posted, 2 Comments) Submitted on 2018-12-12 by Ady TZIDON    

List all the positive integers which are equal to the sum of the digits of their respective cubes.

How many of them are prime?

(No Solution Yet, 1 Comments) Submitted on 2018-12-11 by Ady TZIDON    

Difficulty: 4 of 5 The 100th number (in Sequences) Rating: 5.00
What is the 100th number in this sequence?

7261, 7264, 7265, 7274, 7278, 7302, 7303, 7310, 7317, 7334, 7337, 7336, 7363, 7357, 7366, 7406, 7413, 7425, 7450, 7452, 7462, 7495, 7500, 7563, 7568, 7623, 7644, 7691, 7698, 7723, 7740, 7751, 7803, 7808, 7831, 7844, 7855, 7863, 7894, 7905, 7925, 7935, 7979, 8001, 8169, 8264, 8273, 8310, 8327, 8482, 8524, 8571, 8622, 8661, 8679, 8785, 8839, 8925, 8948, 9077, 9085, 9119, 9164, 9223, 9242, 9347, 9431, 9494, 9537, 9610, 9730, 9783, 9808, 9862, 9980, 10004, 10053, 10254, 10358, 10476, 10535, 10605, 10677, 10731, 10815, 10870, 10891, 10912, 11000, 11080, 11130, 11177, 11201, 11242, 11346, 11379, 11407, 11464, 11507, ?

(No Solution Yet, 2 Comments) Submitted on 2018-12-10 by Math Man    

The plot of sin (x + y) = cos (x2 + y2) looks like a collection of an infinite number of circles. Find the angle of intersection between the smallest two circles in this family of circles.
(No Solution Yet, 2 Comments) Submitted on 2018-12-09 by Danish Ahmed Khan    

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximized?

Source: Project Euler

(Solution Posted, 5 Comments) Submitted on 2018-12-08 by Ady TZIDON    

Consider an ellipse fixed at the origin of the xy-plane having semi-major axis 4 and semi-minor axis 3. A congruent ellipse rolls over the first ellipse without slipping. Initially, they share a common major axis.

Find the locus of focus (the one nearer to the origin) of the rolling ellipse, and calculate the distance traveled by the focus in one revolution (around the fixed ellipse).
(No Solution Yet, 1 Comments) Submitted on 2018-12-07 by Danish Ahmed Khan    

This number N can be expressed as the sum of 1, 2, 3, 4, 5, 6, 7, 8 distinct squares.

Find N and show the 8 possible partitions.

Rem: This fact was discovered by Crespi de Valldaura.

(No Solution Yet, 6 Comments) Submitted on 2018-12-06 by Ady TZIDON    

49 and 1681 are squares with an even number of digits, where both halves are squares, and no zeroes are used.
List all such numbers below 10^10.
(No Solution Yet, 3 Comments) Submitted on 2018-12-05 by Ady TZIDON    

Though this be madness, yet there is method in't.
(Hamlet Act 2, scene 2)

Sunday: 6176
Monday: 62816
Tuesday: 731021
Wednesday: 941336
Thursday: 851340
Friday: 661236
Saturday: ???

What number replaces "???" ?
What is " the method in't "?
(Solution Posted, 4 Comments) Submitted on 2018-12-04 by Ady TZIDON    

List all two digit numbers that if reversed and added to the original number create a perfect square.
(Solution Posted, 6 Comments) Submitted on 2018-12-03 by Ady TZIDON    

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