Word Sums : Maths Setters
Whilst sitting one evening looking through lists of Listener, Tough Crosswords and Magpie mathematical puzzles wondering where my next puzzle for The Magpie would come from and listening to the greatest keyboard player in rock and roll Keith Emerson molesting his Hammond by sticking knives in it I was struck that WORD SUMS had not been used for some considerable time. In fact they’d never appeared in TC or Magpie and the last one was Listener 2411 WORD SUMS IX by Proton some 30 years ago. So I decided it was high time they were used again.
WORD SUMS are a useful tool for teaching mathematical problem solving and I like to use ONE + ONE = TWO and TWO + TWO = FOUR. It never ceases to amaze me that pupils will sit back quite happily having obtained 1 solution to the former totally oblivious to the fact that there are 15 others!
I started by looking at mathematicians EULER ( obviously ), GAUSS, FERMAT, PASCAL etc and wrote a program to find the solutions. I then mixed in maths setters. It is quite fortunate that the majority of maths setters have short pseudonyms and some even have the decency to have repeated letters! I decided to set the mathematicians aside and concentrate on the setters so that if the puzzle was well received then they could form WORD SUMS II!!
The grid was going to be the problem though. In Proton’s puzzles the grids were rectangular and asymmetric. Here however there was a very limited set of WORDS being used and the fact that there were multiple solutions afforded the option of a fig jig amorphous style grid. Solvers would have to work out which of their solutions to use in order to fill the grid. Obviously a unique way in was required and this was provided by 7 x PIE = ELAP. I started with that and gradually built outwards using the two digit entries afforded by MR and AD.
Apparently PIEMAN has not set a mathematical puzzle. I thought he had as in an early issue of The Magpie there was a puzzle using the digits 1 to 4. If I’d bothered to check I’d have found that was by Mr Magoo. The few solutions to MR + MAGOO + PIEMAN = MAGPIE meant that it couldn’t really be overlooked and anyway they were the founders of the magazine. Simon’s also pretty good at Sudoku!!
Apologies to those setters not included especially BRIMSTONE but if you will choose a pseudonym with 9 different letters it makes things kind of difficult!
The following table lists all the solutions
2 x KLAN 2 x 1784 2 x 1786 2 x 1794 2 x 1796
ELAP 3786 3784 3796 3794
LEON 7354 7356 7384 7386
BART 1396 1407 1809
x 5 x 5 x 5 x 5
TREV 6980 7035 9045
PIE 402
x 7 x 7
ELAP 2814
TREV 9513 9613
x 9 x 9 x 9
ARDEN 85617 86517
ARDEN 93675 95482
OYLER 28473 37685
GOOGLY 122148 133167
OYLER 59861
GOOGLY 355389
PROTON 415250
MR 41 45
MAGOO 40922 40922
PIEMAN 368405 368401
MAGPIE 409368 409368
PICC 3866 3866 6833 6833 6877 6877
AD 47 97 74 94 32 92
ILLY 8992 8442 8995 8775 8995 8335
OYLER 12905 12405 15902 15702 15904 15304
June 9th, 2008 at 5:57 pm
I’m not sure this is very fair of me, but you say “afforded the option of a fig jig amorphous style grid” as though it were a bonus. I thought the freeform grid served only as a crude way of providing enough feedback to uniquely identify the solution to each sum.
That said, it is interesting to find out how puzzles come about. I sometimes fancy the idea of setting one but never quite know where to begin (and don’t worry: I’d be no threat to anyone here!).