I was away and offline for this one, in Horsham to look after my mother (91), so bought the Saturday Times for the first time since January 2006. The paper now costs £1.50 and the Listener has moved to the third from last page of the main section. The overall plastic cover that some supermarkets once insisted on had gone so I was able to check that the puzzle was properly printed before purchase.

This is Brimstone’s second Listener but the first, *Family Planning* (theme The Third Man), was not numerical so we may be seeing the emergence of a comparative rarity: a setter who is happy with both digits and letters, one that is perhaps exemplified by Aedites with his almost 50:50 output.

The grid reminded me of *BR’s Home Base* by Wolfram (No.3290, Jan 1995), which consisted of a 10×10 square rotated 45° and where entries were made in base 4. This caught out a number of solvers and prompted the following message to appear in the paper a week later:

**NOTE: A number of readers have inquired about last week’s puzzle, No3290, BR’s Home Base by Wolfram. The puzzle was correct as published.**

I think that this may have been unprecedented at the time, at least in the Times’ era. A few months ago, Oyler said that puzzles with a change of base were out of fashion but I bore it in mind – perhaps there will be a *base jog* later on. I particularly enjoyed those puzzles that Piccadilly set where each row and column were in a different base to be determined, typically from 2 to 12.

At first glance the puzzle looked impossible but then I twigged that we had to consider the grid numbers, clue letters and the remainder, a starting point that I thought most original. They fell into four categories:

**Across only** {5, 11, 13, 15, 16, 17, 20, 22, 23, 24} to match clues {D, G, I, J, K, O, P, Q, S, V}
**Down only **{1, 3, 6, 8, 10, 12, 14, 18, 19, 21} to match clues {C, E, F, L, M, N, R, T, W, X}
**Across and Down** {2, 4, 7, 9} to match clues {A, B, H, U}
**Remainder **{0, 25} to match {Y, Z}

Here are the first fourteen matches that I found, starting with the remainder and Hac:

Hac = B^(UR + Y) but B is greater than equal 2 so Y cannot equal 25 (too big): **Y=0, Z=25**

4dn has seven digits so cannot equal Adn (M + A + Y + S), Bdn (AS) or Udn (HUH): **H=4**

U=2, 7 or 9 but the only fit for Udn (HUH) is 144: **U=9, 9dn=144**

H(4)ac = B^(UR + Y) = 2^9R or 7^9R but the only fit is 512: **B=2, R=1, A=7, 4ac=512**

B(2)ac = – A – B + AS – H = 7S – 13

B(2)dn = AS = 7S = **?1?**

There is only one fit: **S=17, 2ac=106, 2dn=119, Qac(ASH)=476, Vac(R + ASH)=477**

Q and V=11, 16, 23 or 24

Mdn = HU – B – B + UB = 50 and will only fit at 19dn: **M=19, 19dn=50, 7dn=43**

The first part of Dac = B^U + R = 513 and will only fit at 15 or 20ac: D=15 or 20

The first part of H(4)dn = B^(UR + Y)(T – H + E + H) = 512(T + E) =** 5???**: (T + E)=10 or 11 but can only equal 8 + 3 in some order: **4dn starts 5632 and ends 28 (H + ET)**

The first part of A(7)ac = R + ED = **46** and there is only one fit: **E=3, D=15, T=8, 8dn((B + A)(T + HE + S))=333, Oac(AT – E)=53, Cdn(TU) starts 72**

O=5 or 22 but Pac starts B^O and 2^22 is too big: **O=5, 5ac=53, Pac starts 32**

E(3)dn starts **GO=65** then **OD=75**: **G=13, Iac(GRE(E + T))=429**

Neither I, Q nor V=11 so I, Q, V=16, 23, 24 in some order and **all start with**** 4**

The grid now looked like this:

The grid is quite sparse but I shall stop at this point since the full solution will be covered elsewhere. I still have my notes should further explanation be required. The twelve outstanding matches were as follows:

**Across only** {16, 23, 24} to match clues {I, Q, V} and {11, 20, 22} to match clues {J, K, P}
**Down only **{6, 10, 12, 14, 18, 21} to match clues {C, F, L, N, W, X}

The finish was straightforward and I ended by checking the entries for W(21)dn and X(14)dn to give the grid:

The title, BASE = 2×7×17×3 = 714 and JOG = 11×5×13 = 715, which meant nothing to me. The date of this puzzle was 30th May 2009 so 35 years ago would be 30/5/74, which could be represented in the central column and the intersecting number 22/5/51 (1851 or 1951?) could be another relevant date.

Replacing the single digits with letters gave:

Well, I could see **Babe Ruth**, which would account for eight of the eighteen digits to be replaced but nothing else. Being offline and without my reference books, I reverted to my pre-Internet practices and visited Waterstones on Sunday and found in an encyclopædia that **Hank Aaron** passed Babe Ruth’s career home run record of 714 in 1974. A visit to the library on Monday confirmed that the final grid should look like this (highlighting not required):

Henry “Hank” Aaron hit his 715th home run on 8th April 1974 but his own career record of 755 was passed by Barry Bonds on 7th August 2007. If I have ever heard of Aaron, or Bonds for that matter, the names did not linger in my memory but should do so now thanks to Brimstone’s splendid puzzle. The apparent date in the central column was an excellent red herring and no base change was required to finish. The title was a reference to running between bases and gave us the two figures 714 and 715. I can just about see how one would set a puzzle like this, by starting with the highlighted entries in my final grid above, but it must have been terribly time consuming even if computer aided. I wonder what Rhombus would have made of thematic numerical puzzles – they are almost the norm now.

I get nostalgic about the Listener pre-Internet, when most of us struggled against the puzzles in total isolation, so this was a pleasing reminder of those times. As if to rub it in, I returned home after 11 days offline to find nearly 1200 spam e-mails and a mere 8 from friends – thank goodness for MailWasher!