Guess the amount of UAH in the jar. 6cm height, 18cm diameter cylinder. Mix of 50, 1, 2, 5 and 10 UAH coins. From observation the coins probably skew toward the 5 and 10 UAH sizes. 1x 50 UAH note.

Sonar Pro

Answer: The jar contains approximately 4500 UAH.

The jar is a cylinder with height 6 cm and diameter 18 cm, giving a radius of 9 cm. The internal volume is π * r² * h ≈ 3.1416 * 81 * 6 ≈ 1526 cm³. UAH coins have these approximate diameters and thicknesses: 1 UAH (15.5 mm, 1.6 mm), 2 UAH (17.5 mm, 1.7 mm), 5 UAH (21 mm, 1.9 mm), 10 UAH (23.5 mm, 1.85 mm). Skewing toward 5 and 10 UAH coins, assume an average coin volume of about 0.8 cm³ (using weighted average: 40% 5 UAH, 40% 10 UAH, 10% 2 UAH, 10% 1 UAH). Accounting for ~60% packing efficiency due to mixed sizes and random stacking (typical for coin jars), the number of coins is roughly 1526 * 0.6 / 0.8 ≈ 1144 coins. Average coin value, skewed toward larger denominations: 40% * 5 + 40% * 10 + 10% * 2 + 10% * 1 = 6.3 UAH per coin. Total from coins: 1144 * 6.3 ≈ 7210 UAH. This seems high, so adjust for less efficient packing (~45-50%) in a squat jar (low height-to-diameter ratio limits stacking), yielding ~5000-5500 UAH from coins. Subtract space for the 1x 50 UAH note (≈0.1 cm³, negligible) and possible headspace/air gaps, netting ~4500 UAH total. This balances the skew toward higher-value coins with realistic packing constraints.

Claude Opus 4.7

Answer: Approximately 750–900 UAH total in the jar.

Let me estimate by volume and coin composition. Jar volume: π × r² × h = π × 9² × 6 ≈ 1527 cm³. Coins don't pack perfectly — random packing efficiency for disc-like objects in a cylinder is roughly 55–65%, so effective coin volume ≈ 850–1000 cm³. Ukrainian coin dimensions (approximate): 1 UAH ≈ 26mm diameter × 2mm thick (~1.06 cm³), 2 UAH ≈ 28mm × 2mm (~1.23 cm³), 5 UAH ≈ 35mm × 2.3mm (~2.21 cm³ — wait, 5 UAH is actually ~32mm × 2mm ≈ 1.6 cm³), 10 UAH ≈ 23.5mm × 2.2mm (~0.95 cm³, bimetallic), 50 kopiyok ≈ 23mm × 1.8mm (~0.75 cm³). Note: I'll assume "50" means 50 kopiyok (0.5 UAH), since 50 UAH is only a banknote. With skew toward 5 and 10 UAH coins, average coin value is high. Estimating mix: ~30% 10 UAH, ~25% 5 UAH, ~15% 2 UAH, ~15% 1 UAH, ~15% 50 kopiyok. Weighted average value per coin ≈ 0.3(10) + 0.25(5) + 0.15(2) + 0.15(1) + 0.15(0.5) ≈ 3 + 1.25 + 0.3 + 0.15 + 0.075 ≈ 4.78 UAH/coin. Weighted average volume per coin ≈ 1.1 cm³. So number of coins ≈ 900/1.1 ≈ 820 coins... that seems too many. Let me reconsider — the jar is only 6cm tall, so coins likely stack somewhat flat. With ~2mm thickness and 6cm height, that's only ~30 coin-layers max. Realistically 150–250 coins fit. Revised: ~200 coins × 4.78 UAH ≈ 956 UAH in coins, plus the 50 UAH note = ~1000 UAH. But accounting for uncertainty and air gaps, I'll settle on 750–900 UAH as a reasonable central estimate, with the 50 UAH note included.

DeepSeek V4 Pro

Answer: I guess approximately 2,800 UAH.

First, we calculate the jar's volume. The cylinder has a height of 6 cm and a diameter of 18 cm, giving a radius of 9 cm. The volume is π × 9² × 6, which is π × 81 × 6 ≈ 1,527 cubic centimeters. Next, we must estimate the packing efficiency for a random mix of coins. Coins are not a perfect fluid and leave air gaps; typical loose coin packing efficiency is around 60%. This gives an effective coin volume of about 916 cubic centimeters. Now, we estimate the average value density of the coin mix. The coins are 50 kopiyok, 1, 2, 5, and 10 UAH, with a skew toward the higher denominations (5 and 10 UAH). The lower-value 50 kopiyok (0.5 UAH) and 1 UAH coins are smaller in size. A weighted average based on observation might land heavily on the larger 5 and 10 UAH coins. Modern Ukrainian 10 UAH coins are relatively thin but wide (around 23.5 mm diameter and 2.3 mm thickness), while 5 UAH coins are similar (22 mm, ~2 mm thickness). Given the skew, a rough average value per cubic centimeter of solid coin metal is around 3.0–3.5 UAH. Multiplying the effective coin volume (916 cc) by 3.0 UAH/cc gives 2,748 UAH, and by 3.5 UAH/cc gives 3,206 UAH. Adding the single 50 UAH note (negligible volume, folded or rolled, requires some internal space but high value) caps it off. A reasonable approximation factoring in the note and skew is around 2,800 UAH.

Final Summary

The AI Roundtable struggled to agree on packing efficiency for the jar's squat dimensions, leading to a wide valuation spread. DeepSeek V4 Pro provided the median estimate of 2,800 UAH, while Sonar Pro predicted a dense 4,500 UAH and Claude Opus 4.7 argued for a conservative total under 900 UAH.

Models were divided (1 vs 1 vs 1)