GeekDad Puzzle of the Week Solution: Extreme Products

This past week’s puzzle of the week had the most interest (as measured by solutions submitted) in all of the time that I have been posting puzzles. Thank you! Here is the puzzle as presented:

Below is a set of 2400 digits, in an 80×30 grid. Using standard “word find” rules (no wrapping, straight lines only, horizontal / vertical / diagonals are allowed, etc.) strings of 5 digits can be made, and then the digits multiplied together. Somewhere in the set of digits below is the string with the largest 5-digit product, and somewhere in there is the one with the smallest 5-digit product.This week’s puzzle is simple: Find them.

47232925671331615125238689828859497565255424949321558746584659884965785632772411 61742976944757595683231249613656169456845917242697555972916452413694929385738838 11299626565856158962157775633515656622195871923484615926185823219968646799777464 19441598835355413264558243198548946955784645413553115252229153966769919215951755 71312635386898557966852851848326366936174811722489954169316844948913851275494514 91663389357751828294131924699799717113665362813933142129474922977334864133546387 95386897625937567793458377549719185812398373485265571614568834317644295646451646 79621377995391636149964977258581139912683939795623324325632554942882572816284187 27338522689981234679462773798573457464699346966983855382316743952292257232841558 19482568324828454914394833176968424758513951697264928675151998287395939717385262 37718536566382626787228837153549352646158455172349938629348925761318895357237993 96929167127211839619754616238571815947313475231889766613991479933122624295769236 39563195461898153228749821548482529973261844991829125425557168554312142444376933 31174165359123453137568646798477432343412571388962675939747474571469529183524393 23136224999954364931781254576117336162749443551639135317949258843997363549784336 22663562731661418294757488317982248169751571874246132646948841912614459471191174 24138183776168234712552535814277942156342382318125959262797315211699562755989922 12279817814142426954964725999422769515683858267645926238587815159957897411559836 83537962414794646265814889726753842154456466638625331785134233142971642636352132 59595983918412464392448821969294379435622515458423577495242637971929756816116358 54295816224482217172587564745699673679382192357482212844729493864648493887245413 96864356515177526478131117366823871435972289176954528395992274452899145448553722 18872362929135583454742834188757948669471161866317899423198221723452457634789143 33832944319827992253568192175662964122992967739314873683324155991394956471188863 35984489141615963748494967168976715232876752529975299255165617989695895911123242 43687499193798641961998826129147772543879592345416918444426947468417698326249266 32236492896646148141222751528569261573791125287995272319633629474592744756248815 54527945717839234677599737318712362915515936538547987498962971197919691868977454 38676835955531169364361613735265473631142665343484685415915889228342122643197138 73514899513187654564596188147138896997941289726563143686558385638341578822671159

The largest product found was 9x9x7x9x9=45927, and the smallest product found was 1x1x1x2x1=2. They are each highlighted in the image below.

As to how the puzzle was solved, there were two major camps – custom code, and Excel. I don’t believe that anyone admitted to hand-searching for the largest and least products, but there were a few solutions that were close, but sub-optimal. (I’m looking at you, Mr. 99995/11131!) Using Excel seemed the most straightforward (just calculating the products in each direction/diagonal, and applying “max” and “min” functions), but writing code seemed to be more elegant, and more fun as well.

Congratulations to Francis Szalay, who submitted this week’s randomly selected correct submission! Happen not to be Francis? You can still save $10 off a ThinKGeek order of $50 or more using the discount code GEEKDAD81AD.