Ponder This Challenge - June 2017 - Math exercise to 100

Ponder This Challenge:

This month's challenge involves a game that can be played with seven-digit numbers (leading zeroes are allowed), such as the serial number of a bus ticket, a license plate number in Israel, phone numbers, etc.

To play the game, take the seven-digit number and place the four basic operations (+, -, *, and /) and parentheses around and between the digits, using each digit exactly once (the parentheses and operations can be used more than once). Without changing the order or concatenating two or more digits into a larger number, use the basic operations and parentheses so that the answer of the mathematical equation is exactly 100.
Some seven-digit numbers are solvable, like 3141592 which can be solved as (3*1+4)*(1*5+9)+2 or a single digit change of it 3146592, which can also be solved as 3*((-1)+(-4)/6+5*(9-2)), while other seven-digit numbers simply cannot be solved, such as 0314157.

There are 63 ways to change a single digit in a seven-digit number.
Here's the challenge: Find a seven-digit number that is not solvable, but is made solvable by 62 of the 63 single-digit changes.

Bonus '*' if the number is prime.

Solution

• Click here to view the solution

  There are 26 solutions to this month's challenge:

  0155969,0159999,0347743,0397799,0459877,0659949,0739756,0765533,0799557,0946776,0958774,0974767,0987547,3497970,3949810,4778590,7455390,7457890,7559970,7674790,7789540,8826670,8853910,9222970,9499560,9999510.

  And here are the 62 solutions as Serge Batalov sent us, for the two primes:

  for 0397799:
  ((((1+3)/9*7)+7)*9)+9
  ((2*(((3*9)+7)+7))+9)+9
  3*((((3/9+7)*7)-9)-9)
  4*(((((3-9)+7)*7)+9)+9)
  -(5*(((((3+9)-7)-7)-9)-9))
  -(((6*((3/9-7)-7))-9)-9)
  ((((7-3)/9*7)+7)*9)+9
  ((((8*(3+9))-7)-7)+9)+9
  (((9+((3+9)*7))+7)+9)-9
  ((0+1)+((9+7/7)*9))+9
  ((0+2)*(((9*7)*7)+9))/9
  ((((0+4)/9*7)+7)*9)+9
  (0+5)+((9+(7+7)/9)*9)
  (((0+6)+((9+7)*7))-9)-9
  -(((0+7)-9)*((7*7)+9/9))
  -((((0+8)-(9*(7+7)))+9)+9)
  ((((0+9)*9)+7/7)+9)+9
  -(((0+3)-((0+7)*(7+9)))+9)
  -(((0+3)-((1*7)*(7+9)))+9)
  -(((0+3)+(2*(7-(7*9))))+9)
  -((((0*3)+3)-(7*(7+9)))+9)
  ((0*3)+4)*(7-((7-9)*9))
  -(((0+3)+5)*(7/(7-9)-9))
  -((0+3)-((6+(7*7)/9)*9))
  ((0+3)+7)+((7/7+9)*9)
  (((0+3)+8)+7/7/9)*9
  ((((0+3)+9)+0)+7)+(9*9)
  (((0+3)+9)-(1+7)/9)*9
  -(((0+3)-((9-2)*(7+9)))+9)
  ((0+3)+9)/3*((7+9)+9)
  (((0+3)*9)+(4*(7+9)))+9
  (((0*3)+9)-5)*((7+9)+9)
  -(((((0+3)-9)-6)-7)-(9*9))
  ((((0+3)+(9*8))+7)+9)+9
  (0+3)+((9+(9+7)/9)*9)
  (((0+3)+9)+7)+((0+9)*9)
  (((0+3)+9)-(7+1)/9)*9
  (((((0+3)+9)*7)-2)+9)+9
  ((0+3)+9)*(7+(3+9)/9)
  ((((0*3)*9)+7)*(4+9))+9
  (((((0+3)*9)-7)*5)+9)-9
  -((((0+3)-(9*7))*(6+9))/9)
  ((((0+3)+9)+7)+(8*9))+9
  ((((0+3)+9)+7)/9+9)*9
  (((((0+3)+9)*7)+7)+0)+9
  (((((0+3)+9)*7)+7)*1)+9
  ((((0+3)*9)*7)-7)/2+9
  (((((0*3)+9)+7)*7)-3)-9
  (((0+3)+9)-7)*((7+4)+9)
  ((0+3)+9)*(7+(7+5)/9)
  (((0+3)+((9+7)*7))-6)-9
  (((((0+3)*9)-7)-7)*7)+9
  -(((0+3)-(((9-7)*7)*8))+9)
  (((((0+3)+9)*7)+7)+9)+0
  (((((0+3)+9)*7)+7)+9)*1
  (((((0+3)*9)+7)+7)+9)*2
  (((((0*3)+9)+7)*7)-9)-3
  ((0+3)*(((9+7)+7)+9))+4
  -((((0+3)-((9-7)*7))-9)*5)
  (((0+3)+((9+7)*7))-9)-6
  -(((((0+3)+9)/7-7)-9)*7)
  (((((0+3)+9)+7)-7)*9)-8
  
  and for 0765533:
  ((((-1+7)*6)*5)*5)/3/3
  (((((2+7)+6)+5)*5)+3)-3
  (((((3+7)-6)*5)*5)+3)-3
  ((4+(((7+6)+5)*5))+3)+3
  (((((5-7)+6)*5)*5)+3)-3
  (((((6+7)+6)*5)+5)+3)-3
  (((((7+7)*6)+5)+5)+3)+3
  (((((8+7)+6)*5)-5)+3)-3
  (((((9+7)*6)+5)+5)-3)-3
  ((((0+1)+6)*5)-5/3)*3
  ((((((0-2)+6)*5)*5)+3)-3)
  ((0+3)*6)*(5+5/3/3)
  (0+4)+((((6*5)+5)-3)*3)
  (((0+5)*6)+(5+5)/3)*3
  ((((0+6)*6)*5)*5)/3/3
  (0-8+(((6*5)+5)*3))+3
  (((((0+9)+6)+5)*5)+3)-3
  ((((0+7)+0)*5)-5/3)*3
  ((0+7)+(((1+5)*5)*3))+3
  ((0*7)+2)*(5+((5*3)*3))
  (((((0+7)-3)*5)*5)+3)-3
  (((((0*7)+4)*5)*5)+3)-3
  ((0+7)+(((5*5)+5)*3))+3
  ((0+7)+(((7*5)-5)*3))+3
  (((((0+7)+8)+5)*5)+3)-3
  (0+7)+(((9+(5*5))-3)*3)
  ((0+7)+(((6+0)*5)*3))+3
  ((0+7)+(((6*1)*5)*3))+3
  ((0+7)+((6*2)*(5+3)))-3
  (((0+7)/6+3)*(5+3))*3
  ((0+7)*(6+4))+(5*(3+3))
  ((0+7)-6)+(((6+5)*3)*3)
  (((((0+7)+6)+7)*5)+3)-3
  ((0+7)+(6*((8+5)+3)))-3
  ((((0+7)*(6+9))-5)+3)-3
  ((0+7)+(((6*5)+0)*3))+3
  ((0+7)+(((6*5)*1)*3))+3
  (((((0+7)*6)+5)*2)+3)+3
  (((0+7)*(6-5/3))+3)*3
  (0+7)+((((6*5)+4)-3)*3)
  ((0+7)-6)+(((5+6)*3)*3)
  ((0+7)+(6*((5+7)+3)))+3
  ((0+7)+(6*((5+8)+3)))-3
  (((0+7)+((6+5)*9))-3)-3
  (0+7)+(((6+(5*5))+0)*3)
  (0+7)+(((6+(5*5))*1)*3)
  (((((0*7)+6)*5)*5)*2)/3
  (0+7)+((((6*5)+5)-4)*3)
  (((((0+7)+6)*5)-5)*5)/3
  ((0+7)+(((6+5)+5)*6))-3
  (((((0+7)+6)+5)*5)+7)+3
  ((0+7)-6)+(((5*5)+8)*3)
  (((0+7)*((6+5)+5))-9)-3
  ((0+7)+((6+(5*5))*3))+0
  ((0+7)+((6+(5*5))*3))*1
  ((((0*7)+6)*5)*5)/3*2
  (((((0+7)*6)-5)-5)*3)+4
  (((((0+7)+6)+5)+5)-3)*5
  ((((0+7)*6)+5)*(5-3))+6
  (((((0+7)+6)+5)*5)+3)+7
  ((0+7)+(6+5)/(5-3))*8
  (((0+7)*((6+5)+5))-3)-9
  

Solvers

• **Robert Gerbicz (29/05/17 07:10 PM IDT)
• **Serge Batalov (29/05/17 11:21 PM IDT)
• **Uoti Urpala (30/05/17 00:37 AM IDT)
• **Bert Dobbelaere (30/05/17 08:41 AM IDT)
• *Jens Voss (30/05/17 10:56 AM IDT)
• Steven Langerwerf (30/05/17 12:36 PM IDT)
• **Yan-Wu He (30/05/17 01:28 PM IDT)
• **Daniëlle van den Berg (30/05/17 06:48 PM IDT)
• **Alexandr Kozlinskiy (30/05/17 10:39 PM IDT)
• **Reiner Martin (31/05/17 01:00 AM IDT)
• **Sergey Koposov (31/05/17 03:27 AM IDT)
• Oleg Vlasii (31/05/17 08:09 AM IDT)
• **Harald Bögeholz (01/06/17 02:31 AM IDT)
• *Gary M. Gerken (01/06/17 02:55 AM IDT)
• *Shirish Chinchalkar (01/06/17 03:00 AM IDT)
• *Andreas Knüpfer (01/06/17 04:30 AM IDT)
• *Yuval Snappir (01/06/17 07:00 AM IDT)
• **Aviv Nisgav (01/06/17 02:28 PM IDT)
• *Paolo Farinelli (02/06/17 12:03 AM IDT)
• **Aleksey Nekrasov (02/06/17 02:38 AM IDT)
• *Loukas Sidiropoulos (03/06/17 01:54 PM IDT)
• **Hugo Pfoertner (03/06/17 04:04 PM IDT)
• **Hagen von Eitzen (04/06/17 12:16 AM IDT)
• **Florian Fischer (04/06/17 01:55 AM IDT)
• **Motty Porat (05/06/17 01:48 AM IDT)
• **Nigel Brumpton (05/06/17 08:55 PM IDT)
• Fedor Poschmann (06/06/17 11:23 PM IDT)
• **Andreas Stiller (09/06/17 02:46 PM IDT)
• **Benny Poupko (09/06/17 11:58 PM IDT)
• **Leonid Kalmankin (10/06/17 08:31 AM IDT)
• **Stéphane Higueret (10/06/17 08:47 PM IDT)
• **Rickard Björklund (10/06/17 09:50 PM IDT)
• **David Greer (11/06/17 02:47 AM IDT)
• **Yurii Lahodiuk (12/06/17 02:08 AM IDT)
• **George W. Barnett (12/06/17 03:17 AM IDT)
• **Dmitry Kim (14/06/17 03:22 AM IDT)
• *Jesse Rearick (14/06/17 05:30 AM IDT)
• **Jan Rubak (16/06/17 08:24 PM IDT)
• **Peter Gerritson (17/06/17 01:32 AM IDT)
• **David F.H. Dunkley (18/06/17 04:08 PM IDT)
• *Graham Hemsley (19/06/17 05:04 PM IDT)
• **Simo Härkönen (19/06/17 07:13 PM IDT)
• **Armin Krauss (19/06/17 10:14 PM IDT)
• **Alper Halbutogullari (21/06/17 05:25 AM IDT)
• *Nyles Heise (21/06/17 06:59 AM IDT)
• *Vladimir Milovanović (21/06/17 03:45 PM IDT)
• **Todd Will (22/06/17 04:58 PM IDT)
• **Chris Shannon (23/06/17 08:01 AM IDT)
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• *Dario Serino (28/06/17 04:38 PM IDT)
• **Noam & Ayal Zaks (29/06/17 01:01 PM IDT)
• **Tyler Mullen (30/06/17 11:08 PM IDT)