The “math” problems here do not involve numerical addition and subtraction, so don’t break out your calculators. What the “familiar character” actually says to you is “elementary”; this and the range of numbers (1–118) suggests chemical elements. Solvers need to treat these problems as rebuses involving the chemical symbols for the elements with the given atomic numbers:
| 112 + 107 − 41 + 33 | = | CN + BH − NB + AS | CHAS |
| 16 + 67 + 16 | = | S + HO + S | SHOS |
| 14 + 116 | = | SI + LV | SILV |
| 89 + 105 − 48 + 4 | = | AC + DB − CD + BE | ABBE |
| 97 − 19 + 68 + 39 | = | BK − K + ER + Y | BERY |
| 27 + 15 + 15 | = | CO + P + P | COPP |
| 66 + 49 | = | DY + IN | DYIN |
| 99 + 96 − 21 + 78 | = | ES + CM − SC + PT | EMPT |
| 63 − 92 + 7 + 31 + 38 − 33 | = | EU − U + N + GA + SR − AS | ENGR |
| 53 + 116 − 23 + 71 | = | I + LV − V + LU | ILLU |
| 25 + 94 − 93 + 51 + 111 − 35 | = | MN + PU − NP + SB + RG − BR | MUSG |
| 102 + 37 − 5 + 74 | = | NO + RB − B + W | NORW |
| 75 + 22 | = | RE + TI | RETI |
| 34 + 20 + 42 − 95 | = | SE + CA + MO − AM | SECO |
| 9 + 53 + 23 + 2 − 1 | = | F + I + V + HE − H | FIVE |
| 57 + 38 + 85 − 88 | = | LA + SR + AT − RA | LAST |
| 1 + 8 + 29 − 6 + 7 | = | H + O + CU − C + N | HOUN |
| 90 + 118 + 18 − 31 | = | TH + OG + AR − GA | THOR |
| 45 + 32 − 80 + 110 + 113 − 50 | = | RH + GE − HG + DS + NH − SN | REDH |
| 23 + 13 + 71 − 92 | = | V + AL + LU − U | VALL |
Note that the rebuses all lead to somewhat word-like four-letter sequences, but what are they? Solvers need to use their powers of deduction to identify the “familiar character” who says “elementary”. Of course, he is none other than Sherlock Holmes, and these four-letter sequences are all standard abbreviations for short stories and novels in the Sherlockian canon.
The next step is to expand these abbreviations into the full titles of the stories (the rather wide blank spaces suggest that something long belongs there), and use the two numbers in parentheses after the blanks as indices into those titles, selecting two (or, in one case, one) letters, forming another set of element symbols:
| Abbr. | Full Title | Indices | Symbol |
|---|---|---|---|
| CHAS | The Adventure of Charles Augustus Milverton | (38, 16) | NH |
| SHOS | The Adventure of Shoscombe Old Place | (22, 16) | BH |
| SILV | The Adventure of Silver Blaze | (24, 20) | ZR |
| ABBE | The Adventure of the Abbey Grange | (18, 23) | AG |
| BERY | The Adventure of the Beryl Coronet | (27, 18) | NB |
| COPP | The Adventure of the Copper Beeches | (18, 19) | CO |
| DYIN | The Adventure of the Dying Detective | (25, 27) | TC |
| EMPT | The Adventure of the Empty House | (19, 21) | MT |
| ENGR | The Adventure of the Engineer’s Thumb | (25, 28) | RH |
| ILLU | The Adventure of the Illustrious Client | (29, 27) | CU |
| MUSG | The Adventure of the Musgrave Ritual | (22, 25) | RE |
| NORW | The Adventure of the Norwood Builder | (21) | W |
| RETI | The Adventure of the Retired Colourman | (31, 33) | MN |
| SECO | The Adventure of the Second Stain | (20, 22) | CN |
| FIVE | The Five Orange Pips | (5, 9) | IR |
| LAST | His Last Bow | (7, 2) | TI |
| HOUN | The Hound of the Baskervilles | (4, 10) | HF |
| THOR | The Problem of Thor Bridge | (5, 21) | RG |
| REDH | The Red-Headed League | (9, 17) | AU |
| VALL | The Valley of Fear | (15, 12) | RF |
