Number magic

 

Recently I found all the 22 existing ways to put 0 to 9 in the equation of a product such that each number occurs exactly once. And here they are:

5694×3=17082

6819×3=20457

6918×3=20754

8169×3=24507

9168×3=27504

3907×4=15628

7039×4=28156

9127×4=36508

5817×6=34902

3094×7=21658

4093×7=28651

9304×7=65128

9403×7=65821

594×27=16038

495×36=17820

402×39=15678

396×45=17820

715×46=32890

367×52=19084

297×54=16038

927×63=58401

345×78=26910

 

Also, as an extension, did the same after excluding zero:

1738×4= 6952

1963×4= 7852

483×12= 5796

297×18= 5346

198×27= 5346

157×28= 4396

186×39= 7254

138×42= 5796

159×48= 7632

(Dedicated to all my friends who happened to call me a numero-maniac...)

Went through all numbers till 99999999 to find these:

Squares of sums:

(20+25)²=2025

(30+25)²=3025

(494+209)²=494209

(2450+2500)²=24502500

(2550+2500)²=25502500

(5288+1984)²=52881984

(6048+1729)²=60481729

Sums of squares:

12²+33²=1233

88²+33²=8833

990²+100²=990100

9412²+2353²=94122353

 

Syed Iddi Hasan

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