5
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I know that (I found it on Facebook, https://www.facebook.com/search/top?q=tran%20nam%20dung) $2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 = 2024$ and $1234 - 5 + 6 + 789 = 2024$.

$1 + 2 * 3 * 456 + 7 - 8 *90 = 2024$.

What is another expression?

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3
  • 1
    $\begingroup$ I know that ...: May I know how you know? $\endgroup$
    – Syed
    Commented Jan 1 at 14:36
  • $\begingroup$ @Syed I see it on Facebook. $\endgroup$ Commented Jan 1 at 14:46
  • $\begingroup$ Diff of two squares (45+1) * (45-1) $\endgroup$
    – Rabbit
    Commented Jan 1 at 17:57

4 Answers 4

8
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Happy new year to all!

The prime factorisation of the number is:

2^3 11 23

which we can get from

FactorInteger[2024]

Also, 2024 is a Harshad number

Implementation from OEIS

harshadQ[n_] := Mod[n, Plus @@ IntegerDigits@n] == 0;
Select[Range[2024], harshadQ]

It is, also, a Tetrahedral_number

Implementation from OEIS

Accumulate[Accumulate[Range[0, 22]]]

It is, also, a Pernicious number

Implementation from OEIS

Select[Range[2025], PrimeQ[DigitCount[#, 2][[1]]] &] // Last

It can be written as a palindrome minus its digits reversed

6226 - 4202

And, also

77 + Sum[index, {index, 78, 99}]
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opers = {"+", "-", "*"};
Monitor[
     Reap[
      Do[
       Do[
        ts = ToString /@ FromDigits /@ TakeList[Range@9, pd];
        Do[
          exp = StringJoin[Riffle[ts, po]];
           If[ToExpression@exp == 2024, Sow[exp]]
         , {po, Tuples[opers, Length@ip - 1]}]
        , {pd, Permutations@ip}]
       , {ip, IntegerPartitions[9]}]
      ]
     , ip][[2,1]]

{"1234-5+6+789", "12*34*5-6+7-8-9"}
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2
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It is also dodecahedral, n*(3*n - 1)*(3*n - 2)/2, n = 8.

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1
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There seem to be two 2024

list = Flatten[Table[BitXor[b, a - b], {a, 0, 10}, {b, 0, a}]];

p = 
  Catenate @ Map[List, Range @@@ 
    SequencePosition[list, IntegerDigits[2024]], {2}]

{{12}, {13}, {14}, {15}, {60}, {61}, {62}, {63}}

ReplaceAt[x_ :> Style[x, Bold], p] @ list

enter image description here

The sequence was found here

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