Aptitude skill lesson
Coding and decoding: skill lesson
Coding and decoding items give you an artificial rule - shift every letter forward by three, replace each word with a nonsense token, code digits through a table with exceptions - and ask you to apply or reverse it, quickly and without slips. The construct is really letter-position arithmetic plus disciplined bookkeeping, which is why it appears in filing and coding batteries, clerical and records screening, signals and communications tests, and any speeded section where accuracy under a clock is the point. The same habits carry into real work: reference-code systems, batch prefixes and case numbering all reward someone who can apply a rule table without drifting. Everything you practise stays on this device unless you export it.
Published · last reviewed
Applies to Novus Learn 0.1.0
What changed, and when
- , Replaced the body of all 27 non-judgement lessons with construct-specific material: six worked examples each, carrying the actual arithmetic, the actual inference or the actual procedure, plus expanded objectives, practice tips and glossary. Every 'Related Learn topics' link now points at a real page on this site rather than a generic search. The eight workplace-judgement lessons are unchanged.
- , Rebuilt the lesson page around a sticky contents rail, per-section links, previous/next lesson navigation, and two graded checkpoints drawn from the open practice bank.
- , Repaired the aptitude integrations behind the lessons so each one links to skill-specific practice instead of the unscoped fixture engine.
- , Published one lesson for each of the 35 aptitude skill constructs: objectives, worked examples, practice tips, glossary, Learn topic links, and sources.
These 35 skill lessons are authored and revised as one set, so they share one revision history rather than 35 identical dates.
Objectives
Copy link- Convert between letters and positions instantly using anchors (A=1, E=5, J=10, O=15, T=20, Y=25, Z=26) rather than counting from A.
- Solve forward and backward shift codes as signed arithmetic modulo 26, handling wrap-around at both ends of the alphabet without recounting.
- Crack word-to-code substitution items by intersecting pairs of lines that share exactly one word, and explain why code word order carries no information unless the item says it does.
- Apply a conditional coding table with a stated precedence rule, including repeated-digit clauses and mutually exclusive first-and-last conditions.
- Use the reverse-alphabet complement rule - position plus mirrored position equals 27 - instead of writing out a reversed alphabet.
- Detect non-constant rules by computing the shift for every letter and looking for a repeating or position-indexed pattern in the difference sequence.
Checkpoint: does the idea land?
Copy linkBefore the worked examples, check that the objectives above actually landed.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Examples
Copy linkShift codes, wrap-around, and doing it as arithmetic
If FLOWER is coded GMPXFS, each letter has moved forward one place: F to G, L to M, O to P, W to X, E to F, R to S. Applying the same rule, GARDEN becomes HBSEFO. Wrap-around is where the counting method breaks: under the same plus-one rule, ZEBRA becomes AFCSB, because after Z the alphabet starts again at A. Backward shifts are the same operation with a negative sign. If TABLE is coded QXYIB, work in positions: T is 20 and Q is 17, so the shift is minus three. Check it against the awkward letters - A is 1, and 1 minus 3 is minus 2, which becomes 24 after adding 26, and the 24th letter is X. B is 2, minus 3 gives minus 1, which becomes 25, which is Y. L is 12, minus 3 is 9, which is I. E is 5, minus 3 is 2, which is B. Every letter confirms minus three. Candidates who count backwards on their fingers get A and B wrong in about a third of attempts, and they get them wrong silently. Convert to numbers, do the arithmetic, add or subtract 26 if you fall outside 1 to 26, convert back.
Anchors, position sums, and the repeated-letter trap
The five-letter anchor set E=5, J=10, O=15, T=20, Y=25 - taught almost everywhere as EJOTY - puts every letter within two or three steps of a known number, and adding A=1, M=13 and Z=26 closes the gaps. Now a position-sum item. If SUN is coded 54, what is MOON? S is 19, U is 21, N is 14, and 19 + 21 + 14 = 54, so the rule is the sum of the letter positions. MOON is M=13, O=15, O=15, N=14, which sums to 57. The repeated O is the trap: under time pressure candidates count each distinct letter once and produce 42, which is a clean-looking wrong answer. There is a second, deeper point about this rule. A position sum is many-to-one, so different words share the same code - NUS, SUN and UNS all give 54, and so does any other arrangement - which means a sum code can be applied but never reversed. If an item asks you to decode a number back to a unique word, the rule cannot be a plain sum, and you should be looking for something order-sensitive such as concatenated positions or alternating operations.
Word substitution: intersect the lines, ignore the order
Given three coded sentences: 'pit na som' means 'bring the file'; 'som lek dar' means 'file is missing'; 'dar na tuv' means 'missing the envelope'. Work by intersection. Lines one and two share exactly one English word, 'file', and their code sets share exactly one token, 'som', so som means file. Lines two and three share only 'missing', and their codes share only 'dar', so dar means missing. Lines one and three share only 'the', and their codes share only 'na', so na means the. Every remaining token now falls out by elimination: in line one that leaves pit for bring, in line two lek for is, in line three tuv for envelope. So 'bring the envelope' is written with the tokens pit, na and tuv in any order. That last clause is the point most candidates miss: in this format the position of a token carries no information unless the item explicitly states that word order is preserved, so an answer option that lists the right three tokens in a different sequence is correct, and rejecting it is a common way to lose a mark you had already earned. Always work the intersections on paper - three lines of three tokens exceeds what most people can hold reliably in working memory while also doing the elimination.
Conditional coding: read the precedence line first
Rule table: digits 1 to 9 are coded P, Q, R, S, T, U, V, W, X in order, so 1 is P, 5 is T, 9 is X. Three conditions apply. (i) If the first digit is odd and the last is even, code both as A. (ii) If the first and last digits are both odd, code both as B. (iii) Any digit that repeats an earlier digit in the same number is coded Z. Precedence: check (i) and (ii) first - they are mutually exclusive - then apply (iii), judged against the original digits, to the positions not already replaced. Take 35258. First digit 3 is odd, last digit 8 is even, so condition (i) fires and both ends become A. The middle digits are 5, 2, 5: the first 5 is a first occurrence and codes T; the 2 codes Q; the second 5 repeats, so it codes Z. The answer is A T Q Z A. Take 7441. First 7 and last 1 are both odd, so condition (ii) fires and both ends become B. The middle 4s give S then Z. The answer is B S Z B. Take 5359. Both ends odd, so (ii) fires and both are B; the middle 3 codes R, and the middle 5 repeats the original first digit, so it codes Z, giving B R Z B. That last case is the one to study, because whether a repeat is judged against the original digits or against the already-substituted ones changes the answer - and the item's own precedence line, not your instinct, is what decides it.
Reverse alphabet: use 27, never rewrite the alphabet
In a reversed code A stands for Z, B for Y, and so on. Rather than writing out the reversed alphabet under the normal one - which takes twenty seconds and introduces errors - use the complement rule: a letter at position n maps to position 27 minus n, because the pairs always sum to 27. Code MASK: M is 13, so 27 minus 13 is 14, which is N. A is 1, so 26, which is Z. S is 19, so 8, which is H. K is 11, so 16, which is P. MASK becomes NZHP. The same rule answers the position questions that accompany these items. 'Which letter occupies the same position in the reversed alphabet that M occupies in the normal one?' M is 13th, and the 13th letter counted from the end is 27 minus 13, which is 14, so N. 'Which letter is midway between the 5th and the 21st letters of the alphabet?' Take the mean of the positions, (5 + 21) / 2 = 13, which is M - and note that midway questions built on a letter and its own mirror never have an answer, because n and 27 minus n always sum to an odd number. Watch the phrasing too: 'the 7th letter from the right' means position 27 minus 7 = 20, which is T, and misreading left for right is the most common single error in this family.
When the shift is not constant
If CAT is coded DZU, compute each shift separately rather than assuming one rule: C to D is plus one, A to Z is minus one (1 minus 1 is 0, which becomes 26 after adding 26), T to U is plus one. The difference sequence is plus one, minus one, plus one - alternating, not constant. Apply the same alternating rule to BIRD: B plus 1 is C, I minus 1 is H, R plus 1 is S, D minus 1 is C, giving CHSC. A different family indexes the shift to the letter's position in the word. Code FLAME with shifts of plus one, plus two, plus three, plus four, plus five: F is 6 so 7 is G; L is 12 so 14 is N; A is 1 so 4 is D; M is 13 so 17 is Q; E is 5 so 10 is J. FLAME becomes GNDQJ. The general procedure is worth internalising because it never fails: write the numeric difference under every letter pair, then read the difference sequence. Constant means a simple shift; alternating means a two-rule cycle; 1, 2, 3, 4 means a position-indexed shift; and a sequence with no pattern at all usually means the letters have been reordered as well as shifted, which you can confirm by checking whether the coded word contains the same multiset of shifted letters in a different order.
Checkpoint: can you apply it?
Copy linkNow apply it. These come from a later section of the bank, so they are not more of the same.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Practice tips
Copy link- Write the alphabet with its position numbers on your scrap paper before the section starts, once. Every subsequent item becomes arithmetic instead of counting, and the twenty seconds it costs is repaid on the second question.
- Learn the EJOTY anchors so hard that they are not recall but reflex: E=5, J=10, O=15, T=20, Y=25. Candidates who count from A on every letter simply cannot finish a speeded coding section, however accurate they are.
- Treat every shift as a signed number reduced into the range 1 to 26 by adding or subtracting 26. Counting letters near A and near Z is where almost all silent errors in this construct are made.
- On substitution items, write the intersections down. Holding three code lines and three English lines in your head while doing set intersection is exactly the load that produces confident wrong answers.
- Check the repeated-letter or repeated-digit case explicitly on every item, as a separate final step. It is the single most common careless error in the construct, and it costs a mark on an item you had otherwise solved correctly.
- Because these sections are speeded, train accuracy first and speed second: run untimed sets until the alphabet arithmetic is automatic, then time yourself and watch which error type reappears under the clock. Attempts are recorded on this device only, so a messy first pass costs nothing.
Glossary
Copy link- Substitution cipher
- A code in which each letter, word or symbol is replaced by a fixed counterpart. The mapping is the whole content of the code, so recovering the mapping solves every item built on it.
- Caesar shift
- A substitution in which every letter moves the same fixed number of places along the alphabet. Fully described by one signed number, which is why finding the shift for one letter pair solves the item.
- Wrap-around
- The rule that the alphabet is circular: past Z you return to A, and before A you return to Z. Handled by adding or subtracting 26 to bring a position back into the range 1 to 26.
- EJOTY
- The standard mnemonic for the anchor positions E=5, J=10, O=15, T=20, Y=25. Every letter is within two places of an anchor, which turns letter-to-number conversion into a one-step adjustment.
- Complement rule
- In a reversed alphabet, a letter at position n maps to position 27 minus n, since the mirrored pairs always sum to 27. It replaces writing out the reversed alphabet by hand.
- Conditional coding
- A code where a base table is overridden by exception clauses tied to the first digit, the last digit, or repetition. The precedence statement governing which clause wins is the part of the item that must be read first.
- Many-to-one code
- A rule such as summing letter positions, under which different inputs produce identical codes. Such a code can be applied but not reversed, so any decode question implies a different, order-sensitive rule.
- Difference sequence
- The list of signed shifts between each plaintext letter and its coded counterpart. Constant means a simple shift, alternating means a repeating cycle, and 1, 2, 3, 4 means a position-indexed rule.
Sources
Copy link- Worked items written for Novus Learn. Every code, substitution table, rule set and worked answer above is original and invented for this lesson; no published or copyrighted test item is reproduced.
- The EJOTY anchor mnemonic and the reverse-alphabet complement rule are long-standing public study aids in wide general circulation, reproduced here as method rather than as anyone's proprietary material.
- Terminology follows standard, widely published usage in elementary cryptography - substitution cipher, Caesar shift, modular wrap-around.
- Novus Learn aptitude construct registry (catalog seed) for the construct scope and the suite mapping shown in the related links.
- Public educational framing only - not affiliated with any official exam board, publisher or employer.
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