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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    

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