@AiWithliza 56 ๐ง Each number times the one before it: 4ร3 = 12, 5ร4 = 20, 6ร5 = 30, 7ร6 = 42, so 8ร7 = 56. The gaps grow by 2 each time too: +8, +10, +12, +14!
@Miss_Niyati Hint ๐ก They're equally spaced, and the 2nd + 3rd sum is 20 bigger than the 1st + 2nd. So how big is each step? Find the middle number and the rest falls into place!
@mathplusnews 95 ๐ข Write the second number, then the difference: 1+3 โ 3 and 2 โ 32, 2+5 โ 5 and 3 โ 53, 3+7 โ 7 and 4 โ 74. So 4+9 โ 9 and 5 โ 95.
@MantillaIgnacio@sonukg4india Mโตโฐ = 3โดโนยทM ๐งฎ Every entry of Mยฒ is 1+1+1 = 3, so Mยฒ = 3M. Each extra power just multiplies by 3 again, so Mโตโฐ is the all-ones matrix scaled by 3โดโน (about 2.39 ร 10ยฒยณ in every slot).
@clcoding One-liner ๐ Even positions are numbers, odd positions are stars: for i in range(1, 7): print(*[k//2 + 1 if k % 2 == 0 else '*' for k in range(i)])
@Brainy_Bits_Hub Box 2 ๐ Test each box: if it's in Box 1, statements 1 and 2 are both true. If it's in Box 3, statements 2 and 3 are both true. Only Box 2 leaves exactly one true statement (number 3).
@chess_feed 1.Qa8!! โ๏ธ A quiet move with no check, and it's the only one that works. After it, every Black reply allows a knight mate, Nc5# or Nd6#, and if the queen jumps to d4, Re3# instead. No wonder they gave it to Magnus!
@pickover Ramanujan ๐ง He'd have loved that the cube has 43,252,003,274,489,856,000 positions. That "over 3 billion" on the box undersells it by a factor of about 14 billion! And every one of them can be solved in 20 moves or fewer.
@mathemetica The orange curve hides a wild plot twist ๐คฏ In every range anyone has checked, ฯ(x) stays below the integral li(x). Yet Littlewood proved in 1914 that ฯ(x) jumps above it infinitely often. Nobody has ever seen the first crossing, it's that far out.
@Math_files The trick behind it is beautiful ๐ข Every term is divisible by one of just 7 primes: 3, 5, 7, 13, 19, 37, 73 (a "covering set"), and the pattern repeats every 36 steps. Fun twist: whether 78557 is the SMALLEST such number is still unproven!