Key & Compass presents:
Junior Arithmancer
by Mike Spivey

Junior Arithmancer is a Glulx interactive fiction game written with Inform 7 and is © 2018 by Mike Spivey. It was an entry in IF Comp 2018 where it took 7th place overall and 2nd place for Miss Congeniality. At the 2018 XYZZY Awards, it won the Best Puzzles award and was a finalist in the Best Implementation category. This game also placed 46th on the 2019 edition of the Interactive Fiction Top 50 of All Time poll.

In this game, you play as the Academy's first candidate in Arithmancy. The examining committee quickly gives you your exam materials before translating you into the examination room. There, you will use the provided spells to reproduce the numbers on your number sheet to earn points; completing tasks on your task page will also earn you points. Happy spellcasting and good luck!

This solution is by David Welbourn, and is based on Release 2 of the game.

SPOILERS AHEAD. Reading a walkthrough prematurely can sometimes diminish one's enjoyment of an interactive fiction game. Please make an honest effort to play the game before reading this walkthrough.


sta # LectureHall Integers end ret ExaminationRoom


Morkan, Terabox, and Berzia are waiting for you in the lecture hall. You are their first candidate in Arithmancy. Morkan gives you a number sheet, task page, and spell list before he translates you to the examination room.

This game uses left and right panels. The right panel can be toggled with the WINDOW ON/OFF command.

Examination Room

You hear a magical observation system turned on.

> help.

> x sign. (Has the exam instructions.)

> commands.

> i. numbers. tasks. spells. math. x slot.

> know sta. ("Begin a sequence of digits")

> sta 1. (+5 for reaching the first digit in a number sequence.)

Oneinky blackness

> x token. ret.

Examination Room

The instructors think you can't hear them.

> put token in slot. (New spell: INC.)

> know inc. ("Add one to current number.")

> sta 1.

Oneinky blackness

> inc. (+5 for reaching the second digit in a number sequence)

Twosoft, warm red

> ret.

Examination Room

> put token in slot. (New spell: PLU #)

> know plu. ("Add a single digit to current number")

> sta 2.

Twosoft, warm red

> plu 0. inc. (+5 for reaching the third digit in a number sequence)

Threevibrant green

> ret.

Examination Room

> put token in slot. (New spell: MIN #)

> know min. ("Subtract a single digit from current number")

Attempt "2.236":

> sta 2. min 0. inc. plu 3. (+5 for reaching the fourth digit in a number sequence)

Sixbright yellow

> ret.

Examination Room

> put token in slot. (New spell: TIM #)

> know tim. ("Multiply current number by a single digit")

Attempt "2.2360":

> sta 2. min 0. inc. plu 3. tim 0. (+5 for reaching the fifth digit in a number sequence)

> ret.

> put token in slot. (New prefix: CAT)

> know cat. ("Concatenate previous number to front of current number before applying operation.")

Complete "1.41421":

> sta 1. tim 4. cat min 0. plu 7. (+5 for completing a number sequence)

> ret.

> put token in slot. (New spell: DIV #)

> know div. ("Divide current number by a single digit.)

Complete "1.20205":

> sta 1. inc. min 2. cat plu 0. div 4. (+5 for completing a second number sequence)

> ret.

> put token in slot. (New prefix: MOT)

> know mot. ("Truncate current number to its ones digit before applying operation")

Complete 2.71828:

> sta 2. plu 5. cat min 9. mot div 4. tim 4. (+5 for completing a third number sequence)

> ret.

> put token in slot. (New prefix: INV)

> know inv. ("Invert operation")

Complete 3.14159:

> sta 3. min 2. tim 4. cat inc. mot plu 4. (+5 for completing a fourth number sequence)

> ret.

> put token in slot. (New spell: FIB)

> know fib. ("Add previous number to current number")

Complete 0.57721:

> sta 0. plu 5. inv min 2. div 1. mul 3. (+5 for completing a fifth number sequence)

> ret.

> put token in slot. (New spell: SQU)

> know squ. ("Square current number")

Complete 2.23606:

> sta 2. plu 0. inc. tim 2. min 6. fib. (+5 for completing a sixth number sequence)

Sixbright yellow

With six numbers completed, you now have Berzia's vote.

> ret.

Examination room

Merlena casts a gag spell on Teraboz for using a forbidden word.

> z. (Your command is ignored as you listen to the lecture hall drama.)

Teraboz manages to cast a counterspell and can talk again.

> z. (Again, your command is ignored as you continue to listen to the examiners.)

Berzia doesn't understand how Teraboz broke a Council-backed silencing spell.

> put token in slot. (New prefix: ATE)

> know ate. (Denied.)

Since you have earned majority support of the examiners, you'll no longer be helped with spell effects. Remember that according to the sign, using a spell or prefix successfully when constructing a target number counts as proof that you know what the spell effect is.

Complete 3.14159 with just 4 spells via 3, 14, 15, and 9:

> sta 3. ate plu 1. (Spells now lists ATE as "Add ten to current number before applying operation")

> inc. min 6. ret.

Complete 1.20205 in only 4 spells via 1, 20, 20, and 5:

> sta 1. ate plu 9. min 0. div 4. ret.

Complete 2.71828 in only 4 spells via 2, 7, 18, and 28:

> sta 2. plu 5. ate inc. ate min 0. (+3 for Completing four numbers using no more than four spells for each)

> ret.

Complete 0.69314:

> sta 0. plu 6. inv min 3. div 3. ate inc. (+5 for completing a seventh number sequence)

> ret. put token in slot. (New prefix: TAC)

If you experiment, you'll learn that TAC appends the previous number after the current number before applying opration. The reverse of CAT, if you will. By the way, that was the last spell token.

Complete 1.64493:

> sta 1. tim 6. min 2. tac plu 3. (+1 for learning the meanings of all spells and prefixes)

> mot div 3. (+5 for completing an eighth number sequence)

> ret.

Complete 1.73205:

> sta 1. plu 6. min 4. ate fib. div 4. (+5 for completing a ninth number sequence)

> ret.

Complete 1.61803:

> sta 1. inv div 6. mul 3. mot min 8. plu 3. (+5 for completing a tenth and last number sequence)

> ret.

For a perfect score, you'll need to complete all the tasks on your task page. You should have two of them already. But if you don't yet officially know what SQU means yet, because you skipped using know squ before earning Berzia's support, here's one way to do that by constructing 0.693:

> sta 0. plu 6. inv min 3. inv squ. ret.

Visit a dazzling white space (Minus One), then an imaginary-numbered space (the square root of Minus One):

> sta 0. min 1. (+1 for visting a space with dazzling white light.)

> inv squ. (+1 for visiting an imaginary-numbered space.)

> ret.

Complete 1.20205 using just 3 spells, via 1, 20, and 205:

> sta 1. tac tim 2. tac plu 4. (+2 for completing a number in just 3 spells)

> ret.

Complete 2.23606 using five spells:

> sta 2. tac plu 3. mot tim 2. inv div 0. inv min 6. (+4 for completing all ten numbers using no more than five spells for each)

> ret.

Visit a space whose number is greater than 2 billion:

> sta 9. ate plu 9. (28)

> cat min 0. (928)

> tac tim 9. (835,452)

> cat squ. (2,054,226,960; +2 for visiting a space whose number is larger than 2 billion)

> ret.

Visit second and third spaces with dazzling white light, 30 and 900. A number space has dazzling white light if its number is equal to 2n×3n×5n for some positive integer value of n.

> sta 6. tim 5. (+1 for visiting a second space with dazzling white light)

> squ. (+2 for visiting a third space with dazzling white light)

> ret.

Visit a space with pale azure light, 2250. To figure out that this is the number you want, you need to create a working theory how colors are determined by the factors in a number, particularly factors of 2, 3, and 5. Pale azure results when the number equals 5a×3b×2c for positive integer values of a, b, and c where a > b > c, and 2250 = 53 × 32 × 2.

> sta 4. ate inc. squ. tim 5. inv div 2. (+2 for visiting a space with pale azure light)

> ret.

Visit a space with gray light with a hint of violet, such as 350.

> sta 5. tac min 0. tim 7. (+2 for visiting a space whose light is gray with a hint of violet)

> ret.

Do the color tour task:

> sta 3. (Three is green.)

> tim 2. (Six is yellow.)

> inv min 6. (Twelve is orange.)

> div 3. (Four is red.)

> inc. (Five is blue.)

> cat plu 5. (Fifty is violet. +4 points.)

> ret.

You've done it all. Now end this exam:

> tasks. end.

Lecture Hall

The committee votes to accept you, but then Merlena barges in and votes for you as well. Merlena then tries to fire Teraboz, but instead Teraboz turns Merlena into a frog, then quits!

*** Welcome to the Academy ***

> credits





These are the colors associated with the number spaces visited in this walkthrough, plus a few extra:

Zero is special. It is the only integer without any particular color.

Primary colors exclusively use one factor of 2, 3, or 5:

These secondary and trinary colors use two factors of 2, 3, and 5:

White and pale colors use three factors of 2, 3, and 5:

Gray is a result of having prime factors that are not 2, 3, or 5.

All of the above only applies to positive numbers. In brief, negative numbers get the opposite colors from their positive counterparts, for example::

To put that another way:


This is the response to CREDITS at game's end:

Junior Arithmancer is copyright 2018 by Michael Z. Spivey. It may be distributed for free, but not sold or included in any for-profit collection without written permission from the author.

Cover Art: Cody J. Lail Design |

Testing: Arthur DiBianca, Brian Rushton, Andrew Schultz, Walt Semrau, Daniel Spivey

Bug Reports on Release 1: Mike Carletta, Arthur DiBianca, Martin Höfler, John Spivey

Inform 7: Graham Nelson

Extensions to Inform 7: Jon Ingold, Emily Short, Dannii Willis

Junior Arithmancer is dedicated to the memory of David Foreman: teacher, mentor, friend.

Inspirations: The germ of the idea for Junior Arithmancer came from three sources: (1) My own game, A Beauty Cold and Austere, where I always felt there was more that could be done with the number locations, (2) Arthur DiBianca's The Wand, with its simple spellcasting mechanic that actually allows for a huge number of possible spells, and (3) David Fisher's Suveh Nux, in which different spell components combine to create different effects.

If you've enjoyed this game, please let me know at email redacted. Junior Arithmancer is free to play, so my main reward for writing it is feedback from players. Bug reports are also greatly appreciated.

During the game, the response to CREDITS is the same as above but without the Inspirations paragraph.


The game always ends when you cast the END spell. Merlena always shows up to cast her vote and always in your favor, regardless of your perfomance.



The response to SCORE is:

You have earned your-score out of a possible 100 points on your entrance exam in Arithmancy.

Points are awarded as follows:


Exam-only Spells
Arithmancy Spells

When a spell requires a number, that number must be a single-digit number from 0 to 9. You can only use each arithmancy spell once while in the Integer space. Arithmancy spells are restored when you return to the examination room.

Arithmancy Spell Prefixes

Note that while you can reuse spell prefixes, you cannot use more than one prefix per spell.

Other Spells

A couple other spells are mentioned by the examiners soon after you complete your first number. Prefixes are ignored with these spells.

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