ProjectEuler 125

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Problem 125

04 August 2006

The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6^2+7^2+8^2+9^2+10^2+11^2+12^2

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 0^2+1^2 was not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10⁸ that are both palindromic and can be written as the sum of consecutive squares.

Sub Main() Dim sum, i As Long, j As Long, k As Long, dic As Object, max As Long Set dic = CreateObject("scripting.dictionary") For i = 1 To 9999 k = i * i For j = i + 1 To 10000 k = k + j * j If k >= 10 ^ 8 Then Exit For If k = StrReverse(k) Then If Not dic.exists(k) Then If k > max Then max = k dic(k) = k & "=" & Join(Evaluate("transpose(row(" & i & ":" & j & "))"), "^2+") & "^2" sum = sum + k End If End If Next Next Debug.Print "Sum=" & sum & vbCrLf & "Count=" & dic.Count & vbCrLf & "Max:" & dic(max) Set dic = Nothing End Sub

It returns:

Sum=2906969179
Count=166
Max:97299279=312^2+313^2+314^2+315^2+316^2+317^2+318^2+319^2+320^2+321^2+322^2+323^2+324^2+325^2+326^2+327^2+328^2+329^2+330^2+331^2+332^2+333^2+334^2+335^2+336^2+337^2+338^2+339^2+340^2+341^2+342^2+343^2+344^2+345^2+346^2+347^2+348^2+349^2+350^2+351^2+352^2+353^2+354^2+355^2+356^2+357^2+358^2+359^2+360^2+361^2+362^2+363^2+364^2+365^2+366^2+367^2+368^2+369^2+370^2+371^2+372^2+373^2+374^2+375^2+376^2+377^2+378^2+379^2+380^2+381^2+382^2+383^2+384^2+385^2+386^2+387^2+388^2+389^2+390^2+391^2+392^2+393^2+394^2+395^2+396^2+397^2+398^2+399^2+400^2+401^2+402^2+403^2+404^2+405^2+406^2+407^2+408^2+409^2+410^2+411^2+412^2+413^2+414^2+415^2+416^2+417^2+418^2+419^2+420^2+421^2+422^2+423^2+424^2+425^2+426^2+427^2+428^2+429^2+430^2+431^2+432^2+433^2+434^2+435^2+436^2+437^2+438^2+439^2+440^2+441^2+442^2+443^2+444^2+445^2+446^2+447^2+448^2+449^2+450^2+451^2+452^2+453^2+454^2+455^2+456^2+457^2+458^2+459^2+460^2+461^2+462^2+463^2+464^2+465^2+466^2+467^2+468^2+469^2+470^2+471^2+472^2+473^2+474^2+475^2+476^2+477^2+478^2+479^2+48
0^2+481^2+482^2+483^2+484^2+485^2+486^2+487^2+488^2+489^2+490^2+491^2+492^2+493^2+494^2+495^2+496^2+497^2+498^2+499^2+500^2+501^2+502^2+503^2+504^2+505^2+506^2+507^2+508^2+509^2+510^2+511^2+512^2+513^2+514^2+515^2+516^2+517^2+518^2+519^2+520^2+521^2+522^2+523^2+524^2+525^2+526^2+527^2+528^2+529^2+530^2+531^2+532^2+533^2+534^2+535^2+536^2+537^2+538^2+539^2+540^2+541^2+542^2+543^2+544^2+545^2+546^2+547^2+548^2+549^2+550^2+551^2+552^2+553^2+554^2+555^2+556^2+557^2+558^2+559^2+560^2+561^2+562^2+563^2+564^2+565^2+566^2+567^2+568^2+569^2+570^2+571^2+572^2+573^2+574^2+575^2+576^2+577^2+578^2+579^2+580^2+581^2+582^2+583^2+584^2+585^2+586^2+587^2+588^2+589^2+590^2+591^2+592^2+593^2+594^2+595^2+596^2+597^2+598^2+599^2+600^2+601^2+602^2+603^2+604^2+605^2+606^2+607^2+608^2+609^2+610^2+611^2+612^2+613^2+614^2+615^2+616^2+617^2+618^2+619^2+620^2+621^2+622^2+623^2+624^2+625^2+626^2+627^2+628^2+629^2+630^2+631^2+632^2+633^2+634^2+635^2+636^2+637^2+638^2+639^2+640^2+641^2+642^2+643^2+644^2+645^2+646^2+647^2+648^2+649^2+650^2
+651^2+652^2+653^2+654^2+655^2+656^2+657^2+658^2+659^2+660^2+661^2+662^2+663^2+664^2+665^2+666^2+667^2+668^2+669^2+670^2+671^2+672^2+673^2+674^2+675^2+676^2+677^2+678^2+679^2+680^2+681^2+682^2+683^2+684^2+685^2