AMC 8 · 2025 · #2

Grade 4 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

place-valuemulti-digit-arithmeticsystematic-enumeration identify-subproblemssystematic-enumeration ↑ Prerequisites: place-valuemulti-digit-arithmetic

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Problem

Ancient Egyptian numerals are written by repeating symbols, where each symbol stands for a fixed value (single stroke = 1, heel bone = 10, coiled rope = 100, lotus flower = 1,000, bent finger = 10,000, and so on). The system is additive, not positional — the number is the sum of the values of all the symbols shown. Given a combination of 1 bent finger, 4 coiled ropes, 2 heel bones, and 3 single strokes, find the number it represents and match it to one of the five choices.

Pick an answer.

(A)

1,423

(B)

10,423

(C)

14,023

(D)

14,203

(E)

14,230

AMC 8 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Make a Systematic List

The cleanest path is Tool #2 (Systematic List): walk through the four distinct symbol types from largest value to smallest, tally how many of each appear, and multiply count × value. Because the Egyptian system is additive, the answer is just the sum of these four products — no place-value juggling needed. Tool #3 (Eliminate Possibilities) is a great second pass for multiple-choice: the absence of the lotus flower (1,000) forces the thousands digit to be 0, which alone narrows the five choices down to (B) 10,423, giving us an independent check on our computation.

1STEP 1

Sort the symbols by value, largest first, and count how many of each appear so no group is missed or double-counted.

bent finger: 1, coiled rope: 4, heel bone: 2, single stroke: 3

2STEP 2

Multiply each count by its symbol's value — a single digit times a power of ten, so just attach the matching number of zeros.

1 × 10,000 = 10,000; 4 × 100 = 400; 2 × 10 = 20; 3 × 1 = 3

3STEP 3

Add the four partial values — no two share a place, so there are no carries and the total is 10,423.

10,000 + 400 + 20 + 3 = 10,423

4STEP 4

Cross-check by elimination — the bent finger means at least 10,000 and no lotus flower forces a 0 in the thousands place, so only (B) fits.

10,423 = (B)

Answer

10,423

The bent finger contributes 10,000, so the answer must be at least 10,000 — that immediately rules out (A) 1,423. There are no lotus flowers (worth 1,000 each), so the thousands place must be 0, which fits 10,423 but not any of 14,023, 14,203, 14,230. The hundreds digit comes from 4 ropes (= 400), the tens digit from 2 heel bones (= 20), and the ones digit from 3 strokes (= 3); reading the answer left-to-right as 1, 0, 4, 2, 3 matches 10,423 digit by digit.

💡Key takeaway

This AMC 8 problem only needs Grade 4 place value and multi-digit addition you already know!

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