Game Guide
The five Sangaku demo tablets solved with the method rather than the answer, from 5 plus blank equals 9 to the two step 4 times blank minus 2 equals 22.
Sangaku were real objects. During the Edo period, Japanese mathematicians and enthusiasts carved geometry and arithmetic problems into wooden tablets and hung them at shrines and temples, frequently without the solution, as an offering and a challenge to whoever came next. MyRin borrows the form: a tablet, an expression, one missing value, and the quiet expectation that you will work it out rather than be told.
The free browser demo has five tablets. This walkthrough goes through all five, but the answer is the least interesting part of each one. What matters is which of two methods you reach for, because only one of them survives contact with the harder levels.
Here is the MyRin short for Sangaku. Seeing the tablet and the four choice row in motion makes the format obvious in a few seconds.
Every demo tablet shows an expression with a box for the missing value and four numbers to choose from. That format invites substitution: take the first choice, plug it in, check, move on. Substitution is reliable and it is also a dead end, because its cost grows with the number of options and the number of blanks. Four choices and one blank is four checks. Two blanks and four choices each is sixteen.
Inversion does not grow that way. Instead of testing values, you rearrange the expression so the box is alone on one side, then compute once. One blank or two, four choices or ten, inversion costs the same. The demo is easy enough that you can afford to practise the slower habit here, which is the only reason to bother.
The choices are 3, 4, 5 and 6. Inverted, the box equals 9 minus 5, which is 4.
Trivially easy, and precisely for that reason it is the right place to say the inversion out loud: "the box is nine minus five". You are building a reflex, and reflexes are built on problems where you do not need them.
The choices are 5, 6, 7 and 8. This is the first tablet where inversion needs a moment of care, because the box sits on the subtracting side. The box equals 15 minus 8, which is 7.
Many people find it faster to rephrase the subtraction as an addition instead: "8 plus what makes 15?" That is the same operation from the other direction, and if it feels quicker to you, use it. Counting up from the smaller number is a genuinely faster route for most people than subtracting down from the larger one.
The choices are 6, 7, 8 and 9. The box equals 21 divided by 3, which is 7.
Worth noticing: 21 is not in the three times table for any of the wrong choices, so a magnitude check alone eliminates nothing here, and the choices are deliberately tight. This is the first tablet where guessing from the shape of the numbers does not help and you have to actually divide.
The choices are 5, 6, 7 and 8. This is the tablet that catches people, because the box is the divisor rather than the result, and the reflexive move is to compute 24 divided by 4.
That reflex happens to give the right answer here, 6, but for the wrong reason, and the coincidence will not hold in the installed game. The correct inversion when the unknown is the divisor is: if 24 divided by the box equals 4, then the box equals 24 divided by 4. Say why rather than just taking the number, because when the equation becomes 24 divided by the box equals 3, the same reflex has to be reasoned about rather than recalled.
The choices are 4, 5, 6 and 7, and this is the only genuinely two step tablet in the demo. The answer is 6, and the order of undoing is the whole lesson.
The expression does two things to the box: multiply by 4, then subtract 2. Undo them in reverse order. First undo the subtraction: 22 plus 2 is 24. Then undo the multiplication: 24 divided by 4 is 6. If you undo in the original order instead, dividing 22 by 4 first, you get 5.5 and then nothing sensible, which is exactly the error the tablet is built to produce.
Reverse order undoing is the single most transferable idea in this game. It is the same rule that governs unwinding any nested operation, and the harder levels of the installed version lean on it constantly.
Inversion first does not mean ignoring the four options. Once you have computed a value, the choice row is a free check: if your answer is not among them, you made an arithmetic slip, and you know it before you commit. That is a much better use of the options than treating them as candidates to test.
The magnitude filter is also worth keeping for the harder tablets. If an expression needs a value somewhere around thirty, any choice below ten or above sixty can be discarded before you compute anything exactly. Under time pressure that often reduces four options to two, and two options are cheap to resolve even by substitution.
This is arithmetic fluency with an algebraic edge. The pure calculation involved is small, nothing here goes beyond a times table, and that is deliberate: the difficulty lives in manipulating the structure of the expression rather than in the size of the numbers. Recognising that the unknown sits in the divisor position, and knowing what to do about it, is early algebraic reasoning wearing very light clothing.
For the same reason the game works well for a wider age range than its arithmetic suggests. A child who can divide 24 by 4 can attempt every tablet in the demo, and an adult who can do that instantly still has to think about tablet five. If you want the version with pressure attached, Arithmetic Blitz is the timed version of the same skill, and the installed game adds a clock and 600 levels; the demo is the untimed place to fix the method first.