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Mathematical equations and Latin squares: two kinds of constraint Vibedu CounsellingBook Free Counselling
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Mathematical equations and Latin squares: two kinds of constraint

One subtest is arithmetic reasoning; the other is pure deduction from a grid. Neither rewards computing everything.

9 min read

The other two core-module subtests are mathematical equations and Latin squares. They look unrelated and they train the same habit: work from the constraint that pins the most down.

Mathematical equations. These are reasoning items dressed as arithmetic. The mathematics in them is school level; the difficulty is in seeing what the relationship demands before you start calculating. Three habits carry most of the marks:

  • Estimate before you compute. If the options are far apart, an order-of-magnitude estimate eliminates three of them in seconds and you never do the arithmetic at all.
  • Work backwards from the options when the algebra is messy. Single-choice means one of the five is true. Substituting is often faster than solving.
  • Watch units and direction. Per-unit, per-cent-of-what, increase-versus-increase-to. Most wrong answers on this kind of item are right arithmetic on the wrong quantity.

Latin squares. A grid in which each symbol appears exactly once in every row and every column, with some cells filled and some blank. You deduce the missing ones. It is the same logic as a sudoku and none of the arithmetic.

The technique is the same one that solves every constraint puzzle: start where the choice is smallest. Find the row, column or symbol with the fewest possibilities left, resolve that, and the resolution shrinks the choices elsewhere. Do not start at the top-left because it is the top-left.

Two working rules that save time:

  • Scan by symbol, not by cell. Pick one symbol and ask where in this row it can possibly go. That usually gives a forced placement faster than staring at an empty cell.
  • Mark eliminations, not guesses. A cell you have proved cannot be X is worth more than a cell you think might be Y, and it never sends you down a wrong branch.

Neither subtest rewards finishing everything. The items get harder as they go; the marks on an early item and a late item are the same. Bank the ones that fall out quickly.

Do this now

Five to ten minutes. This is the part that moves your band.

Twenty minutes, split. Ten on five arithmetic-reasoning items where you must write your estimate before your answer and compare the two. Ten on one 4×4 or 5×5 Latin square, solved by writing down, for each placement, the constraint that forced it. If you cannot name the constraint, you guessed — undo it and find the one that was forced.

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