Shedletsky’s Self-Checking Formula Cabinet
The cabinet
In Roblox, Shedletsky built a cabinet with sixteen formula drawers and a three-wheel combination lock. Every drawer label determines one whole-number value. Some labels are single expressions; others show two equal expressions or use definitions from the brass reference plate.
One matched pair of notation marks has been replaced by a different valid pair. Every digit, letter, operation, decimal point, and drawer position is still correct. The damaged expression is still valid mathematics and still has a whole-number value.
THE CABINET KEEPS ITS OWN KEY.
Do not decide which label is damaged merely because it looks unusual. Use the numerical structure of the cabinet.
Brass reference plate
Function
Determinants and dot products
Complex numbers
Combinations and factorials
Random variable
Conventions
is the numerical angle measure in degrees. Trigonometric limits use radians.
. If units cancel, use the remaining numerical value.
Shedletsky’s Self-Checking Formula Cabinet
Cabinet inspectionValue record
Copy each printed drawer value into the corresponding position.
| A | B | C | D |
| E | F | G | H |
| I | J | K | L |
| M | N | O | P |
Evidence record
| Check | Drawers or structure checked | What fails |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 |
Printed label: ____________________________________
Corrected label: __________________________________
Corrected value: __________
Questions
Use separate paper for calculations and the four-place proof.
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Read every label
Evaluate all sixteen labels exactly and record their values in the matching 4 × 4 grid.
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Find the damaged drawer
Identify the one corrupted drawer. Give at least three independent numerical checks that all implicate it; visual suspicion is not evidence.
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Repair the notation
Replace exactly one matched pair of notation marks. Record the printed label, corrected label, and value; change nothing else.
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Open the cabinet
Find the three-digit combination and show it in at least four structurally different places after repair.
I opened the lock — reveal the cabinet’s hidden mechanisms
Material revealed after the lock opens
The complete inspection
Extension A · Sixteen appearances
The repaired cabinet contains exactly sixteen deliberately built-in appearances of its key. Find and classify all sixteen.
Extension B · One mark, five readings
The same vertical stroke appears in several labels but does not always mean the same thing. Find the drawers showing a determinant, set cardinality, absolute value, complex modulus, and evaluation at a specified value.
Extension C · The cabinet’s two half-charges
Pair each drawer with the drawer directly opposite it through the center. The key is odd, so it cannot split into two equal whole-number charges. What two consecutive totals alternate among the eight opposite pairs?