Problems & Puzzles: Puzzles

Puzzle 1203 2025 On Dec 127, 2024 Emmanuel Vantieghem wrote: 1) 2025 = (12-3-4)*(5*6+7+8)*9=(9*(8*7-6-5)*(4+(3-2)*1) 2) 2025 = (3^(11-7))* 5^2=(2+3)*5*((7-11+13)^(-17+19))   From some other places and communications I found also that: 3) 2025 = 45^2 = 5^2*9^2 = 5^2*3^4 = 1^6*3^4*5^2 4) 2025 = 40^2+20^2+5^2 5) 2025 = (1+2+...9)^2 6) 2025 = (20+25)^2 7) 2025 = 1^3+2^3+...+9^3 = (1+2+...9)^2 8) 2025 = 12×3+(4+5)×(6+7)×(8+9). 9) 2025 = 9×8+76+5^4×3+2×1. Q. Perhaps you can add some other interesting expressions for 2025.

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From Jan 4 to 10, 2025, contributions came from Michael Branicky, Jeff Heleen

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Michael wrote:

Here are some expressions I found:

2025 = 1^2 * 45^(6/3), using digits 1-6;
 

2025 = 1^2789 * 45^(6/3), using digits 1-9;
 

2025 = (1 + 7 - 8*2 + 9) * 45^(6/3), using digits 1-9;

2025 = 9*75*3*1, using all five odd digits in reverse order.

 

Here is one due to Scott Duke Kominers (http://www.scottkom.com/):
 

"2025 = ((20)*2+5)^2; it's the only four-digit number to have such a decomposition abcd = ((ab)*c+d)^2."

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Jeff wrote:

2025 = (3^3)^2 + (2^2 x 3^2)^2

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