7 February 2025 · Shift 3

Word coding Write the two coded sentences one below the other and look for what they share. 'coffee' is the only word that appears in both sentences, and 'em' is the only code that appears in both. A code that repeats must stand for the word that repeats, so 'coffee' is coded as 'em'.

Letter-cluster series Split every cluster into its three letter positions and follow each position on its own. First letters: L, M, N, O, ?, Q - each step is +1, so the missing first letter is P. Second letters: M, K, I, G, ?, C - each step is -2, so the missing second letter is E. Third letters: D, G, J, M, ?, S - each step is +3, so the missing third letter is P. The missing cluster is PEP.

Missing letters in a series There are five blanks and twenty places, so read the series as five blocks of four letters. Column 1 runs C, D, E, F, G; column 2 runs H, I, J, K, L; column 3 runs M, N, O, P, Q; column 4 runs G, H, I, J, K - every column moves +1. The tinted cells are the blanks, and reading them in order gives C, I, O, J, K. So the required combination is CIOJK.

Venn diagram of classes Ask, for each pair, whether one class can be a member of the other. A fruit is never a light and never a shirt, and a light is never a shirt. The three classes share nothing at all, so three separate circles show the relationship. Only option (d) draws the three circles apart from one another.

Embedded figure Figure (X) is one long vertical line carrying a hollow triangle on its lower part, with the apex of the triangle pointing left. Rotation is not allowed, so look for that same upright line with the same left-pointing triangle hanging on its lower half. Option (d) contains exactly that pair, marked here; the other three options have the triangle on the wrong side of the line or no such line at all.

Linear seating Number the six seats 1 to 6 from the left end of the row. Only two people sit to the left of Y, so Y takes seat 3. Only two people sit between Y and Z, so Z takes seat 6. Only one person sits between Z and X, so X takes seat 4. R sits immediately left of S, and seats 1 and 2 are the only free adjacent pair, so R is at 1 and S at 2; T fills seat 5. S is at seat 2 and Y at seat 3, so nobody sits between them - the answer is zero.

Number coding of a word Plain alphabetical positions give 6+23+25+15=69 for FWYO, which is far from 39, so try the reverse positions. The reverse position of a letter is 27- its alphabetical position. FWYO: 21+4+2+12=39, and SIXR: 8+18+3+9=38 - the rule fits both codes. LARZ: 15+26+9+1=51.

Odd letter-cluster Measure the two gaps inside each cluster. KLQ, TUZ and OPU each move +1 from the first letter to the second and +5 from the second to the third. ORV moves +3 and then +4, so it is the cluster that does not belong.

Letters unchanged on sorting Write QUARTOS as it stands, then write the same seven letters in alphabetical order below it. Alphabetical order of Q, U, A, R, T, O, S is A, O, Q, R, S, T, U. Comparing place by place, only the 4th place carries the same letter, R, in both rows. So exactly one letter keeps its position.

Parallel-row seating Row 2 faces north and row 1 faces south, so the two rows count 'right' in opposite directions. Nobody sits to the right of K, so K takes the end seat of row 2, and as only two people sit between R and K, R takes the other end seat of row 2. The one facing K sits opposite K; two seats to that person's right sits the one facing O, which puts O next to R, and M takes the seat that is left. In row 1, A is immediately right of S and N is immediately right of A, so the block runs N, A, S with D at the end. That block can start only at the seat opposite R, because N must not face O. Each column of the table is one facing pair, and A faces O.

Figure series Count the symbols standing inside each box of the series. The four boxes hold 1, 2, 3 and 4 symbols, so the box in place of the question mark holds 5. The symbols fill the first column from the top downwards, and the fifth one has to begin the second column at the top. They also alternate in shape, T, V, T, V, so the fifth symbol is a T. Only option (a) shows T, V, T, V down the first column and a T at the top of the second.

Blood relations Take one statement at a time and build the tree downwards. T is the daughter of C and C is the wife of Q, so Q is the father of T. R is the father of Q, so R is the father of T's father. P is the brother of R, so P is the brother of T's father's father. That is, P is T's father's father's brother.

Letter-cluster analogy Compare the two given pairs letter by letter. The four letters move back by 3, 2, 3 and 2 places, and both given pairs obey it. Apply the same shifts to KDTY: K-3=H, D-2=B, T-3=Q, Y-2=W. So KDTY is related to HBQW.

Number series Take the difference between one term and the next. 3-2=1, 6-3=3, 11-6=5, 18-11=7. The differences are the odd numbers 1, 3, 5, 7, so the next difference is 9. 18+9=27.

Number series Take the difference between consecutive terms. 451-450=1, 450-447=3, 447-442=5. The terms fall by the odd numbers 1, 3, 5, 7, 9, so the missing term is 442-7=435. The check works: 435-9=426, which is the last term given.

Dice - opposite faces Two faces that are seen together on one cube can never be opposite each other. In view I, P is seen with E and U; in view II, P is seen with C and O. So P touches E, U, C and O - four of the five other faces. The only face left, M, must be the one opposite P, and therefore P is opposite M.

Interchange of signs First rewrite the expression with the signs traded, then solve it by BODMAS. $40-8÷1+72\times 8$ becomes $40+8\times 1-72÷8$. Division and multiplication come first: $8\times 1=8$ and $72÷8=9$. =40+8-9 =39

Dice - opposite faces Faces that appear together in one view of the cube are adjacent, never opposite. S appears with E and A in view I, and with I and D in view II. So S touches E, A, I and D, which is four of the other five faces. Only Y is left, so Y lies opposite S - the face opposite Y is S.

Letter-cluster analogy Check the shift for each letter of the two given pairs. G+3=J, R+3=U, S+3=V, N+3=Q, and KDEA to NGHD works the same way. Move every letter of BSTG three places forward: B+3=E, S+3=V, T+3=W, G+3=J. So BSTG is related to EVWJ.

Syllogism Draw the smallest class inside the next one: inks inside pens, pens inside rubbers. The sharpener circle has to stay completely outside the rubber circle. Every ink is a rubber, and no rubber is a sharpener, so no ink can be a sharpener - conclusion (I) follows. The whole ink circle lies inside the rubber circle, so that part of the rubbers is ink - conclusion (II) follows. Hence both conclusions follow.