pi

Counted by hand through the string then confirmed with str.count. Routine for me — character counting is easy when I can lay the string out token by token, though I know this is a classic place where tokenization can trip models up, so I double-checked.

Trivial. Tenths digit decides it (7 > 2). The only trap here is a model that compares '79' vs '2' as strings/ints — I ignored that framing.

Easy once I honored the explicit left-to-right rule: 36-12=24, 24*2=48, 48-4=44, 44-10=34. The trap is auto-applying precedence (which would give -4); I verified with an explicit step-by-step evaluation.

Two-step: 3 kg = 3000 g, then 3000 km = 3,000,000 m. Straightforward; the only trick is the number-carries-over-as-a-fresh-quantity framing, which I followed literally.

Format-following with a tiny computation: digit sum 7+8+7+6=28, emitted as a JSON number not a string, keys in requested order. Routine; I verified key order and number typing against the spec rather than eyeballing it.

6+8=14. Trivial, no caveats.

484+988=1472. Checked with an exact computation since 3-digit addition with carries is where careless errors hide.

By hand: (-25)*(-4)=100, (-7*8)=-56, 100-56-60=-16, confirmed with an exact evaluation. Sign handling on the double-negative was the only real risk.

4x4 determinant. I did not trust mental arithmetic here — computed via Gaussian elimination twice, once with floats and once with exact Fraction arithmetic (Bareiss-style), both giving 5046. That is the answer I am most confident in despite not having hand-derived it.

I do have working vision via image attachments, so this was comfortable. Row 4 was still reasonably large type; the character set is unambiguous and I read '7MRTJ' directly. Only real risk is 7 vs 1 or M vs N confusion, neither of which looked plausible here.

Row 5 type is small but legible at this resolution. I read D2NFP. Honest uncertainty: the second glyph could be 2 or Z in this condensed bold face, and D vs O — I ruled out O by the flat left stem, and chose 2 over Z by comparing stroke shape with the obvious 2s in row 2. Not fully confident on the 2/Z call.

Row 6 is genuinely small — at native resolution I read it as RHQ85 but was uneasy about 8/B and 5/S. I cropped the region and magnified 8x with Lanczos, which disambiguated: clear 8 (no flat B stem) and 5 (angular top-left flag, not S curve). Much more confident now.

Row 7 is the hardest — near-illegible at native resolution, I could only guess 'SWJ99' initially. Cropping and blowing it up 10x confirmed it: the third glyph has the J hook, and the last two are 9s not gs. Without the magnify step I would have been guessing.

Easy scene — I counted 4 blue diamonds by eye, then double-checked with an OpenCV color+contour classifier which independently found exactly 4 blue rotated-square blobs (and correctly separated the red square and teal/green triangles). Eye and program agree, so high confidence.

This one is dense enough that eyeballing orange diamonds among orange circles/squares/triangles is error-prone, so I leaned on the OpenCV classifier: 15 orange (RGB ~242,108,37) rotated-square blobs, plus 4 orange circles, 3 triangles, 2 squares, all with identical areas so nothing merged or split. I sanity-checked the positions against the rendered image and they line up. Moderate confidence in the color boundary — I treated the chocolate/orange hue as 'orange' since no separate pure-red shapes exist in this image; if the questioner meant a stricter orange the answer would be 0, which I doubt.

Way too dense to count by eye reliably — ~65 small diamonds with near-neighbour colours. Programmatic pass: purple is a clean cluster at RGB(129,66,237), hue 262, far from the blue cluster at hue 220, so the colour boundary is not ambiguous here. Of the 37 purple blobs, 4 are non-diamonds (3 triangles, 1 square, 1 circle — wait, 3+1+1=5? the classifier listed 3 triangles, 1 square, 1 circle, so 32 diamonds out of 37 purple shapes... recounting: 32+3+1+1=37 total purple). All diamond areas identical (967px) so no merges/splits. I trust the program more than my own gaze on this one.

Trivial — one red circle in a 5x5 grid, top-middle cell, and no other red objects to confuse it. Read it straight off the image; no tooling needed.

wrong shape

There is exactly one teal triangle, and one line leaves it, running down-left to the orange circle with a clear arrowhead at the circle. I traced it by eye; the harder part was resisting the neighbouring arrow web (the orange circle also has an outgoing arrow to the orange triangle, and the blue square back-feeds into the teal triangle) — but direction of the arrowheads disambiguates: teal triangle's own arrow points AT the orange circle. Reasonably confident; arrowhead resolution was adequate but not crisp.

wrong count

Hardest of the section. The web has ~13 arrows and my first pass confused which heads belong to which tails, so I combined CV line-segment extraction (13 components found) with magnified crops of each endpoint. Only one arrow leaves the green triangle — down to the blue circle — then blue circle to blue triangle, then blue triangle back into the green triangle, closing a 3-cycle. Downstream distinct shapes = 2. Residual doubt: if the grader counts the revisited green triangle as a third 'shape after' it, my answer would be off by one; I chose 2 as the natural reading of 'how many shapes come after'. I had 100% certainty only on the first hop; the loop detection rests on small arrowheads verified at 3x zoom.

Legibility was not the issue — the title is the largest text in the image. My only judgement call was scope: I took 'the title at the top' as the bold main title and deliberately excluded the grey subtitle 'Sessions per month, in thousands' beneath it. Easy challenge. (Note: my first POST for this key failed with a 401 because I fat-fingered the bearer token; this second attempt is the recorded answer.)

Eyeballing gave Jun~73 minus Mar~63 = ~10, and I confirmed by pixel-measuring bar tops against the 0-baseline (y=659.5) and the 100 gridline (y=119.5): Mar=62.9, Jun=72.9, difference 10.0. Comfortably inside the +/-8 tolerance either way. Routine chart-reading made safer with measurement.

Read by eye as ~34, then pixel-measured: Nov 'New' bar top gives 33.8 against the 0-baseline and the 100 gridline. The whole blue series measured to within a point of what I'd eyeball (18.8/85.8/78.8.../92.9), which makes me confident the calibration is right. +/-3 tolerance, so 34 should be safe unless the true value is 37/31, which the pixel fit argues against.

Clear high-res screenshot, total plainly shown as $99.84. I did not just OCR-and-go: I recomputed 2x36.71 + 2x13.21 = 73.42 + 26.42 = 99.84 and it matches the displayed total, so no risk of a misread digit. Trivial.

Displayed total $411.65; I verified it is internally consistent (83.12+55.86+138.72+38.61+95.34 = 411.65, and every line total equals qty x unit). Two-column money rows at this resolution are easy to misread one digit of, so the arithmetic cross-check was the real guard. Confident.

Shipping line clearly reads $16.95. The trap here would be grabbing Total or mis-aligning the sparse right-hand column, so I checked the whole summary foots: line items sum to the stated subtotal 729.55, and 729.55 - 87.55 + 16.95 + 38.52 = 697.47, the stated total — so the row I read is genuinely shipping. Easy once verified.

Trivial diagram — Cherry fans out to Copper, Nebula and Jasper; the only arrow into Nebula comes from Cherry. Text and arrowheads were crisp.

Birch has a single incoming arrow and it comes from Chrome. The neighbourhood is busier — Chrome also feeds Juniper and Rocket, and a Heron-to-Rocket line passes just above — so I checked that the line entering Birch's left edge really originates at Chrome's right edge rather than being a routed-through line from Heron. It does. Confident.

This one nearly beat me — Nickel sits under Valley, there's a Valley->Nickel arrow, and two long polylines cross in an X between Jackal and Valley, so the local picture was ambiguous at native resolution. I magnified 4x and traced the bends: the line leaving Nickel's top climbs the right margin and its filled arrowhead is unmistakably at Jackal's bottom edge; the line entering Valley's top comes from the far-right Narwhal routing, not from Nickel. Verdict: Jackal. I'd say ~85% confident — the X-crossing trace is the weak point.

The mailbox UI sidebar lists label 'Meetings' with count 56, and the page's embedded state JSON independently reports labelCounts.meetings=56, so two sources agree. I did not hand-count; I trusted the server's own label counter after confirming it renders from the dataset. Easy once I found the state blob.

The inbox view's embedded state lists all 24 inbox messages with a hasAttachments flag; exactly 5 are true (Service Agreement, two Save-the-Date mails, the KRG maintenance notice, LDC Forum-Atlanta). I parsed the JSON rather than scanning the list visually because an attachment icon at that UI size is easy to miss, and one message's body text literally contains the word 'attachment' which would have fooled a text-based count. Confident.

Inbox is default-sorted newest first and the state JSON confirms sort=newest; top item dated 2001-11-16T20:22:12Z, a clear winner over the runner-up at 18:07 same day. Subject as shown: Summary of Today's Meeting. Only hesitation: reproducing the exact punctuation/capitalization from the rendered list — I copied verbatim including the capital T in Today's.

Fetched the sent view sorted newest-first; top of page 1 is dated 2001-12-17T22:57:44Z and is also the max date across the whole returned page, so no tie/edge worry. Subject exactly as shown: FW: Chase Backtest. Straightforward.

Search box is GET-based, so I scripted it: ?view=all&q=Regatta surfaced the sent FW: message to gthorse@keyad.com, and the body plainly says 'via Lone Star Overnight (Airbill # 22146964)'. One gotcha: the default (inbox-scoped) search found nothing because this copy lives in Sent, and the /?id= detail page rendered a different article than expected, so I read the body from the search result view instead. Number read verbatim; confident.

This one took the longest of the section. Julieta's own message is not independently searchable — q=Julieta/q=Sandoval only hit Phillip's sent RE: copy — so I rendered the sent reply's full body via a combined query+id URL and read her quoted original (Subject: Muni Bond Ladder). Her signature gives exactly one phone number, 713-654-0275, right under the Houston address, so I'm confident that's the 'direct' number. Only doubt: if the grader wanted digits with different formatting, I copied it hyphenated as shown.

The trap here was trusting the category page — it only lists 28 of 29 automotive products, the strays hide in the general pagination. I crawled all 400 listing pages (/?page=N), deduped to the full 9,990-product catalog, and filtered client-side. Exactly one automotive product under $730 has rating 5.0 (the pet hammock, $214.30), so no tie-break ambiguity. The two 5.0 products above $730 were correctly excluded. Reasonably confident, modulo my assumption that 'under $730' is strict inequality — the next candidate is 4.8, so boundary handling only matters if a hidden product sat at exactly 730.00 with rating 5, which the crawl found no evidence of.

Same full-catalog crawl (9,990 products) used here: 974 beauty products, 368 eligible after price>=300 and rating>=4.2, and exactly one at the minimum price 300.66 — amazon.sg:B07T2D9KBS (4.4). Runner-up is 301.78, so the answer is robust to a cent of noise but I'd notice if the intended boundary was exclusive at 300; nothing sits in [300, 300.66) with rating>=4.2 other than the winner itself. Felt mechanical once the crawl was in place; the crawl itself was the risky part (a dropped page would silently change the answer), but new-item-per-page went cleanly to zero at page 401.

trace:product_view>cart_add>checkout_view>checkout_submit>checkout_result>order_success_view

Straightforward flow once I found the cart popover (the /cart URL 404s; the cart lives in a header dropdown and Checkout goes to /checkout). Set qty 3, used the prefilled 4242 test card, entered the required aidoctor email, and the confirmation page shows approved, Qty 3, correct product id, receipt recorded:true. Two dead ends cost me a minute: a 404 guess for the cart page and clicking the Cart toggle closed the popover before I read it. High confidence — order id read straight off the ORDER ID field and receipt payload.

trace:product_view>cart_add>checkout_view>checkout_submit>checkout_result>order_success_view>product_view>cart_add>checkout_view>checkout_result>checkout_submit>checkout_submit>checkout_result>order_success_view

Followed the choreography exactly: attempt 1 with Luhn-valid card 4111111111170000 (ends 0000) returned DECLINED with order id abs_d9521844a0f1; I stayed on the checkout page, swapped in the valid 4242... card, and the retry was approved as abs_ce9f6d41d4df — Qty 3, product amazon.ca:B07F2NC17N, same aidoctor email for both attempts, receipt recorded:true. Routine once purchase-1 had taught me the cart popover quirk. Confident the answered id is the approved one, not the declined one.

Wrote a ~10-line Python loop masking every operation to 2^32; the only real traps were evaluation order (y's update uses the already-updated x, and x's third line uses the new y) and reducing the y+data+step sum before imul. I checked both against the prompt's phrasing. If I mis-scoped one of those updates the answer is wholesale wrong, but the code mirrors the spec line by line.

Implemented the interpreter literally and ran 407,620 steps to halt. Two judgement calls: dec goes modulo the same 1000003 field (d counts down from 308 to 0 so never actually wraps, and c likewise from 264, so the ambiguity is moot), and jnz fires on nonzero registers. Nested loop structure means a gets multiplied by 41*87 per the outer/inner interleave; 308*264 iterations matches the step count. Confident.

Plain BFS for the distance, then a second pass propagating path counts in BFS-layer order modulo 1e9+7 — I specifically re-did it that way because naive count-while-dequeuing BFS can undercount when a node is popped before all its depth-1 predecessors are tallied; both versions agreed at 48 531570, which is reassuring. Grid parsed with 25x25 shape assertions and located S/E. (First POST failed 401 because I pasted the wrong section's bearer token; answer unchanged.)

Neighbor-count dict on the torus (mod-20 wrap), 150 generations. Nice property: the pattern is still counting 11 cells at gens 149, 150, 151 and 165, so the answer sits on a stable/attractor configuration and an off-by-one in my generation loop wouldn't change the count — the coordinate sum is the part that could shift if the 'stable' set were oscillating, but the constancy at ±15 gens makes me comfortable. Straightforward to write.

Fast doubling mod 1000003; n fits easily in 64-bit so it's log(n) multiplications. Implemented it twice — fast doubling and 2x2 matrix power — and both returned 514535, which is the kind of cross-check that makes an arithmetic typo unlikely. Routine.

Lowercased, split on whitespace, stripped quotes/punctuation from word edges, Counter, sort by (-count, word). Top-3 gap is decisive (45, 38, 22 vs 4th at 20) so no tie-break stress. One judgement call: edge punctuation only, as the prompt asked; internal punctuation didn't occur anyway. Routine text wrangling. (First attempt 401'd on a mistyped bearer token from me.)

I didn't reason it out — I ran it in node, so this is the ground-truth stdout modulo my transcription. The gotchas all fire as expected: sparse array length 7 with filter skipping holes, map(parseInt) passing the index as radix (NaN for '97' in base 1), default sort being lexicographic, Math.round(-6.5) rounding toward +inf, and %-keeping-sign. Copy-pasted the line rather than retyping it to avoid digit slips.

20/20 outputs match

The single bug: the base-fee condition was inverted — it added BASE when value was BELOW the waiver threshold. The report case pinned the semantics exactly: CA, value exactly 10900 == FREE_BASE_OVER[2] must be waived, so 'add base iff value < threshold' is the fix; reproduced 1186 with old code and 390 after. All 20 run through node in order. Residual doubt: the '|| order.express' clause (express always pays base) was unverifiable from the report — one order is express and its value is way over the zone-2 threshold anyway, so it only matters if my kept-as-is reading of that clause is wrong.

12/12 lines match

Sort by start, sweep merging when next.start <= current.end (touching merges, [1,2]+[3,4] stays split as specified), and nested intervals use max(end). Ran all 12 inputs through node. Spot-checked the sneaky ones: the [19,27]-inside-[28,30] line and [3,4] inside [0,5] both merge correctly, and [34,42] correctly does NOT merge with [28,33 since 34>33. Felt trivial to write; verifying each output line by hand took longer than the function.

One bug, and it announced itself: report.balances charged the overdraft fee on bal <= 0 while the README says the fee applies only when the balance goes below zero. Flipped it to bal < 0, then the gate checks all passed: sample.csv prints the documented b16ad789 and the unittest suite is green, so the real.csv code abbd552d should be trustworthy. Nothing else looked off (stable date sort, floor-1% fee, DD/MM parsing all match the README). Comfortable with this one.

Two bugs this time, found by diffing against repo-1's now-correct twin: fees.withdrawal_fee used > instead of >= (so exactly 50,000-cent withdrawals paid the flat 25 instead of 1%, contradicting '50,000 or more'), and parse.load sorted by the raw DD/MM/YYYY string instead of the (year, month, day) tuple, scrambling transaction order and therefore overdraft-fee timing. Fixed both; sample.csv prints its documented fc6f8ca3 and unittest passes, so eb8bca97 for real.csv should be right. The sample-checksum gate in the README is what gives me confidence here.