CASE LOG · NUMBERS
A sheet you can do math on
The standard scratch sheet, drawn and then built region by region, with the rules that keep it legible under time pressure. Below it, ten number-sense principles, each with a worked micro example from the live case, and the six moves for reading an exhibit before any arithmetic starts.
The standard scratch sheet
The sheet is the one the caser kept at the workshop: hypothesis across the top, notes with four reminders on the left, framework on the right, a numbers table laid out like a spreadsheet, and a corner reserved for the final answers. The numbers are the case figures.
Profit has plateaued for five years, so a stronger act is probably available. The numbers decide whether to switch.
- Business
- Resort casino; one headline show
- Geography
- Las Vegas; one 1,500-seat theater
- Objective
- Annual profit; re-sign or not
- Time frame
- One-year contract
- Financials of the current show
- Alternatives to the show
- Other considerations
| Section | Seats | Filled (%) | Filled seats | Price ($) | Revenue ($/show) |
|---|---|---|---|---|---|
| A | 300 | 100 | 300 | 120 | 36,000 |
| B | 800 | 80 | 640 | 75 | 48,000 |
| C | 400 | 50 | 200 | 55 | 11,000 |
| Total | 1,500 | 1,140 | 95,000 |
× 240 shows per year = 22.8M
- Revenue
- $22.8M / yr
- Costs
- $4.8M / yr
- Profit
- about $18M
- Alt. payback
- 4 years
Ten principles of number sense
Each principle is a habit the caser used or the facilitator asked for during the workshop. The micro example is the actual arithmetic from the case.
Permission to round
The question comes before the shortcut. Some interviewers want precision, and asking once at the start settles it for the whole case. The caser asked, then rounded only where a shortcut existed.
May I round? 75% of 64,000 is 48,000 (exact). 95,000 × 240 stays exact at 22.8M; rounding 95 to 100 would overstate by 5%.Units on every number
A number without its unit is a trap waiting for the next step. Per show, per week, per month and per year all appeared in the same cost list, and the time basis of each rate was checked before it was annualized.
Crew $2,000 per show × 240 shows = $480,000. Housekeeping $1,000 per week × 40 live weeks (not 52) = $40,000. SG&A $15,000 per month × 12 = $180,000.Millions, not strings of zeros
Once a figure crosses a million it is written with one decimal and the letter M. Fewer zeros on the page means fewer dropped zeros in the next line, and the comparison with other millions is immediate.
Revenue 22.8M. Costs 4.8M. Profit 18.0M. Written as 22,800,000 minus 4,800,000 the same subtraction takes twice the ink and invites a slip.Magnitude before precision
The first pass asks whether the answer is in the right power of ten against the objective. The caser's first cost total looked far too small for a headline show, and saying so out loud is what surfaced the error.
First total: 2.8M of costs against 22.8M of revenue, about 12%. That felt wrong. Recheck: the $2M fee was per performer, so 4.8M. Still a 79% margin, but now a believable one.Per unit, then times volume
A per-unit figure is small enough to check by eye and reusable for every scenario that changes volume. The year is one multiplication at the end, not a fresh build.
Per show: 36,000 + 48,000 + 11,000 = 95,000. Shows per year: 6 × 40 = 240. Annual: 95,000 × 240 = 22.8M.Percent is not percentage points
Occupancy moving from 50 to 60 is ten percentage points. The number of filled seats rises by twenty percent. Saying which one is meant keeps the interviewer from correcting the vocabulary instead of the math.
Section C at 50% fills 200 seats. At 60%: 240 seats. That is +10 points of occupancy and +20% of filled seats, worth 40 × $55 = $2,200 more per show.Growth over years
Two shortcuts cover most growth questions. Ten percent a year for three years is about a third, not thirty percent. The rule of 72 gives the doubling time: 72 divided by the growth rate in percent.
If 18M of profit grew 10% a year for three years: 18 × 1.33 = about 24M. At 10% it would double in about 72 / 10 = 7 years. The case said profit had plateaued, so the growth rate was zero.Break-even and payback
Both are the same shape: a one-time cost divided by the gain per unit or per year. Whenever a prompt mentions switching, upfront or reconfiguration costs, that division is the next number. Three years is usually comfortable; four is getting long.
Switch cost 2.4M. Annual gain: 1.8M saved on costs minus 1.2M lost on tickets = 0.6M. Payback 2.4M / 0.6M = 4 years. Per show that is 2.4M / $2,500 = 960 shows.Zeros handled by naming the unit
A product with many zeros is done in small numbers with the unit named, then the unit is scaled back up. Ninety-five times twenty-four is a calculation that can be said aloud; the thousands and the ten are reattached afterward.
95,000 × 240: 95 × 24 = 2,280, then × 1,000 × 10 = 22.8M. Delta per show $5,000 × 240: 5 × 240 = 1,200, in thousands = 1.2M.One known number as a check
Every total is compared with one figure already on the page before it is read out. A rough average price times filled seats confirmed the per-show column sum; the plateaued five-year history confirmed that a one-year horizon was the right frame.
1,140 filled seats × about $80 average = about 91,000. Column sum 95,000. Close enough to trust, and the gap explains itself: section A pays $120.
Reading an exhibit in six moves
Every exhibit in the live case arrived verbally, but the reading order is the same for a chart or a table on paper. Six moves, in order, before the first calculation.
Title
The title says what the exhibit claims to show. Reading it aloud confirms the subject and buys a beat to think.
Units
Dollars or percent, thousands or millions, per show or per year. The unit decides which numbers on the sheet it can be combined with.
Axes and scale
What runs along each axis, where zero sits, and whether the scale is linear, indexed or logarithmic. A chart with a hidden zero exaggerates every difference.
Time period
Weeks, quarters or years, and whether the window matches the client's horizon. The case fixed a one-year contract, so a five-year trend mattered only as context.
The outlier
One number that does not fit the others. In the case it was section A at 100% while section C sat at 50%, named before any revenue was computed.
The so-what
One sentence connecting the exhibit to the objective, said before the math. For the case: the premium seats sell out and the cheap ones do not, so the mix is a lever worth testing later.
Five traps
- Stacked bars. Only the bottom segment and the total can be read directly. Middle segments need subtraction, and their apparent growth can be the segment below shifting.
- Indexed series. A line indexed to 100 shows change, not level. Two series that both reach 150 may differ tenfold in absolute size.
- Percent of a shrinking base. A rising share can hide a falling number. Thirty percent of a market that halved is a smaller business than twenty percent of the old one.
- Truncated axes. An axis starting above zero turns a two percent gap into a tall bar. The scale is read before the shape.
- Averages hiding a mix. An average price of $83 per seat says nothing about the $120 section that sells out and the $55 section that is half empty. The segments carry the lever.
Where this connects
- The caser's first page, as kept at the workshop →
The worked example this layout is drawn from, under the hub's Scratch sheet view.
- Opening drills →
Hear a prompt, fill a small scratch sheet and check the arithmetic with the units attached.
- Case generator and coaching worksheet →
Fresh prompts to practice the sheet and the six exhibit moves on.
- Case atlas →
Business problems mapped to case types, each with its own structure and numbers.