NEMERTES: the decisive experiment

An untimed, adaptive online test of fluid reasoning, from the NEMERTES research edition NM1.0 (November 2026), for ages 16 to 80. Every problem shows two machines, Left and Right. A machine changes a board of pieces (circles, squares and triangles in black, white, blue and orange) by a rule: which pieces it acts on (by shape, color, position, neighbors or the whole board), what each does (turns a color, becomes a shape, disappears, moves or copies itself) and whether it acts once or again and again until nothing changes. The two rules differ in one part only. A few examples show what each machine does; on the start board both give the same result. You make one change to the start board, putting a piece from the tray on an empty cell or taking one away, so that the two machines give different results. There is no list of answers: every change that splits the machines is right. Every problem is built by code from a formal grammar of 41,200 rules, and an independent solver, a separate program that sees only what the problem shows, proved for every problem in the bank that every rule of the grammar fitting a machine's examples gives the same right changes, and that they are the key's. Its four families are the four kinds of machine: change in place, disappear, move and copy.

It opens with 4 practice problems, one per family, the examples shown on this page. Answer each and lock it: you see at once whether you were right, a change that is right and the reasoning. Practice is never scored. Then the scored problems come one at a time, each chosen from your answers so far: the four kinds of machine take turns, ten problems each, and in each the model picks one of the problems that tell most about your level, for 40 scored problems; from level 8 up, a level opens only once you have solved the one below it consistently. Make your one change on the start board, a piece put on an empty cell or a piece taken away, and lock it; a locked answer cannot be changed, and you cannot go back. If you cannot decide, you may leave a scored problem unanswered: it scores no point. Nothing tells you whether a scored answer is right, and your result appears the moment the last one is locked.

Every problem has one of twelve levels, from IQ 70 to 184, about ten points apart, computed by the model NM-D04 from how the problem is built: what it takes to read both rules, how hidden their difference is (from shape against color, at level 1, to two conditions of which one differs, applied again and again until nothing changes, from level 11), how precise the change must be (the share of all possible changes that are right, from about half at level 1 to under one in a hundred at the top), how many steps ahead the machines must be followed before they part, and how much is on the board (six by six cells, seven by seven from level 11). Every problem's difficulty lies within five points of its level's. These difficulties are the model's assumptions until real first attempts are analyzed. Four more levels, up to IQ 225, are being built: their problems take hours each to find, and they will come with a later bank.

From the problems you were given and your answers to them, by the provisional model NM-D04: each problem is a Rasch item with its level's assumed difficulty, and the four kinds of machine take turns, ten problems each. The model's estimate of your ability is shown as an IQ (mean 100, SD 15) with its 95% interval; it uses a Jeffreys prior, which holds no score back toward the average. A problem scores its point when the change you lock makes the two machines give different results. A problem left unanswered scores no point. Two people with the same number of right answers can receive different problems and different results. In the simulation of the bank, the estimates were within about 3 to 6 IQ points of the truth from IQ 70 to 180, with a reliability of 0.89 and a retest correlation of 0.90; at IQ 190, above the hardest level released, the scale holds an estimate back by several points. NEMERTES is a research edition: no human calibration has been done yet (N = 0), so a score is a provisional position on the model's scale, not a percentile of the population, and no percentile is reported. The scale is reported up to IQ 184+, the level of the hardest problems released; an estimate below IQ 70, the level of the easiest, is reported as below IQ 70. Beside the IQ, as THETIS does, your result gives the rule complexity: the level, from 1 to 12, of the problems you solve half the time. It describes what you solved, so it depends on no population norm.

A high score must rest on consistent success at the levels below it (the ladder, from 5 November 2026, as THETIS has above IQ 180). From level 8 up, NEMERTES climbs one level at a time: no problem above the level being cleared is given until it is solved consistently, which takes at least three right answers at that level, from at least two families, with at least two in three of its problems right; very consistently, from 160 up, at least four right, with at least three in four of its problems right. So a score of 147 or more needs level 8 (problems of IQ 142) solved consistently, 160 or more level 9 (IQ 153) very consistently, 180 or more level 11 (IQ 173) very consistently and 184+ level 12 (IQ 184) very consistently. Until then a score is held just below the next step, however well the answers above it went; the result and the certificate say so.

NEMERTES is untimed. From the moment you begin, your attempt stays open for 90 days: work in as many sittings as you like, on any device, with your private link, and you come back to the problem you left. Each answer is locked on the server as you give it. An attempt still open after 90 days is scored with the answers locked by then, provided it has at least 40 scored answers; otherwise it ends without an IQ.

Yes, whenever you like once your previous attempt is finished, and every attempt is on scored problems you have never been shown. Every problem counts as seen the moment it reaches your screen, together with every problem of the same two rules, under this email or another registered with the same name and year of birth; no later attempt meets it again. Practice is the same four problems every time: the examples shown on this page. Every attempt has its own fee. From the second attempt, the certificate is issued by the test author, who sends the one you need, as a rule that of your best result; your score is shown at once as before. Register every attempt with the same email. Only first attempts go into the research data on the test's norms.

The US$19.99 fee, paid through PayPal before the attempt opens, covers one attempt: the practice problems with their explanations, the 40 scored problems, your result with its PDF certificate, and a copy by email. Each retake has its own fee.

Yes, from 5 November 2026. IQ 147 or higher meets the criterion of the Nereid Society and IQ 160 that of the Mesopelagic Society. Just below the criteria, IQ 135 to 146 qualifies for associate membership of the Nereid Society and IQ 184+ for subscription to the Aphotic Society. Every membership, associate members and subscribers included, has a one-time fee, with no annual dues. The criteria of the Aphotic, Hadal and Exocosm Societies lie above NEMERTES's scale, which ends at IQ 184+. Your best result counts, as for THETIS, and it counts as NEMERTES's ladder holds it: a high score must rest on consistent success at the levels below it (see “How is my score worked out?”). NEMERTES is a research edition, scored with provisional model norms until enough first attempts are in, and the author reviews every result before admission.

To build NEMERTES's norms from real people. They are re-estimated from first attempts only, anchored on examinees whose IQ is known from a supervised test, such as a Wechsler or Stanford-Binet scale given by a psychologist, Raven's or Cattell's test given under supervision, or a high-IQ society's supervised admission test. Giving yours is optional, and it never changes your own result: it only helps place the problems on the IQ scale for everyone. Only attempts with a clean integrity record are used, and a new calibration is applied only when, checked on people it was not fitted on, it comes closer to their known IQs than the scale in force. If you allow it, the author may write to you to confirm the score.

The answer keys and the bank never leave the server, and your result never shows which scored problems you solved. Only the problem on screen ever reaches your browser: the next one is chosen on the server after you lock your answer, from the answers you gave, so there is no list of problems to look up in advance, and a retake is always on problems you have never been shown. Each problem is drawn on the screen with a faint watermark of your name and certificate ID. While a problem is on screen, the test page records leaving the test window, screenshot shortcuts (Print Screen, Windows+Shift+S, Command+Shift+3, 4 or 5), printing (Ctrl+P or Command+P), copy, right-click and drag attempts, and AI assistant add-ons that insert themselves into the page; the server keeps its own times (when each problem was shown and when its answer was locked) and notes right answers given moments after a long absence, and many right answers in a few seconds. As on THETIS, it checks the answer pattern against the difficulty of the problems you were given (a pattern unlikely for one person at your level is noted, as is a result at the top of the scale), and practice problems are recorded too. The record is sealed when you finish, and its fingerprint is printed on your certificate. The author's integrity report of each attempt lists all of it, problem by problem. None of this changes a score, and unusual results are reviewed, never judged automatically. An untimed test cannot rule out every form of help, which is why you declare that you will work alone.

Your private link (shown when your test is ready, and kept in this browser) reopens your test on any device, at the problem you have reached. If you lose it, use “Recover my test” with the PayPal Transaction ID from your receipt and the email you registered with. Every locked answer is on the server.

Yes: the four example problems above, one for each kind of machine, with a right change and the reasoning of each. They are the practice problems that open every attempt, and they are never scored.