All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Palindromic and Tautonymic IV (Posted on 2010-12-27)
Make a list of distinct positive integers that are obtained by assigning a different decimal digit from 1 to 9 to each of the capital letters in bold in this expression.

(A+B)C + (D+E)F + (G+H)I

Determine the smallest and the largest positive palindromes. What are the smallest and the largest prime number? How many amongst the abovementioned list are tautonymic numbers?

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution Comment 1 of 1

10   LgPal=0:LgTau=0:LgPr=0
20   SmPal=9999999999999999999999999
30   SmTau=9999999999999999999999999
40   SmPr=9999999999999999999999999
110   V\$="123456789":H\$=V\$
115   repeat
120     gosub *Permute(&V\$)
130     A=val(mid(V\$,1,1))
140     B=val(mid(V\$,2,1))
150     C=val(mid(V\$,3,1))
160     D=val(mid(V\$,4,1))
170     E=val(mid(V\$,5,1))
180     F=val(mid(V\$,6,1))
190     G=val(mid(V\$,7,1))
200     H=val(mid(V\$,8,1))
210     I=val(mid(V\$,9,1))
220     V=(A+B)^C+(D+E)^F+(G+H)^I
230     S=cutspc(str(V))
240     Pal=1
250     for J=1 to int(len(S)/2)
260       if mid(S,J,1)<>mid(S,len(S)+1-J,1) then Pal=0
270     next
280     if Pal=1 and V>LgPal then LgPal=V:LgPalS=V\$
290     if Pal=1 and V<SmPal then SmPal=V:SmPalS=V\$
300     if prmdiv(V)=V or prmdiv(V)=0 then Pr=1:else Pr=0
310     if Pr=1 and V>LgPr then LgPr=V:LgPrS=V\$
320     if Pr=1 and V<SmPr then SmPr=V:SmPrS=V\$
330     if len(S) @ 2=0 then Tau=1:else Tau=0
331     Diff=0
332     for J=2 to len(S)
333      if mid(S,J,1)<>mid(S,1,1) then Diff=1
334     next
335     if Diff=0 then Tau=0
340     for J=1 to int(len(S)/2)
350       if mid(S,J,1)<>mid(S,int(len(S)/2)+J,1) then Tau=0
360     next
370     if Tau=1 and V>LgTau then LgTau=V:LgTauS=V\$
380     if Tau=1 and V<SmTau then SmTau=V:SmTauS=V\$
700   until V\$=H\$
710   print "("+mid(SmPalS,1,1)+"+"+mid(SmPalS,2,1)+")^"+mid(SmPalS,3,1)+"+("+mid(SmPalS,4,1)+"+"+mid(SmPalS,5,1)+")^"+mid(SmPalS,6,1)+"+("+mid(SmPalS,7,1)+"+"+mid(SmPalS,8,1)+")^"+mid(SmPalS,9,1),SmPal
720    print "("+mid(LgPalS,1,1)+"+"+mid(LgPalS,2,1)+")^"+mid(LgPalS,3,1)+"+("+mid(LgPalS,4,1)+"+"+mid(LgPalS,5,1)+")^"+mid(LgPalS,6,1)+"+("+mid(LgPalS,7,1)+"+"+mid(LgPalS,8,1)+")^"+mid(LgPalS,9,1),LgPal
730   print "("+mid(SmPrS,1,1)+"+"+mid(SmPrS,2,1)+")^"+mid(SmPrS,3,1)+"+("+mid(SmPrS,4,1)+"+"+mid(SmPrS,5,1)+")^"+mid(SmPrS,6,1)+"+("+mid(SmPrS,7,1)+"+"+mid(SmPrS,8,1)+")^"+mid(SmPrS,9,1),SmPr
740    print "("+mid(LgPrS,1,1)+"+"+mid(LgPrS,2,1)+")^"+mid(LgPrS,3,1)+"+("+mid(LgPrS,4,1)+"+"+mid(LgPrS,5,1)+")^"+mid(LgPrS,6,1)+"+("+mid(LgPrS,7,1)+"+"+mid(LgPrS,8,1)+")^"+mid(LgPrS,9,1),LgPr
750   print "("+mid(SmTauS,1,1)+"+"+mid(SmTauS,2,1)+")^"+mid(SmTauS,3,1)+"+("+mid(SmTauS,4,1)+"+"+mid(SmTauS,5,1)+")^"+mid(SmTauS,6,1)+"+("+mid(SmTauS,7,1)+"+"+mid(SmTauS,8,1)+")^"+mid(SmTauS,9,1),SmTau
760    print "("+mid(LgTauS,1,1)+"+"+mid(LgTauS,2,1)+")^"+mid(LgTauS,3,1)+"+("+mid(LgTauS,4,1)+"+"+mid(LgTauS,5,1)+")^"+mid(LgTauS,6,1)+"+("+mid(LgTauS,7,1)+"+"+mid(LgTauS,8,1)+")^"+mid(LgTauS,9,1),LgTau
790   end

finds

Palindromic
(4+5)^3+(6+9)^1+(7+8)^2 = 969
(1+3)^9+(2+5)^8+(6+7)^4 = 6055506

Prime
(4+5)^3+(6+8)^2+(7+9)^1 = 941
(1+4)^2+(3+6)^5+(7+8)^9 = 38443418449

Tautonymic
(4+7)^3+(5+8)^2+(6+9)^1 = 1515
(4+7)^3+(5+8)^2+(6+9)^1 = 1515

(apparently there's only one tautonym, serving as both smallest and largest)

 Posted by Charlie on 2010-12-27 16:35:06

 Search: Search body:
Forums (0)