Reasoning · Grade 2-2 Rules and Defined Operations
Problem
76 goes through 42 to 8: length 2.
Following the rule one multiplication at a time and stopping at a single digit gives the count directly.
3.OA.C.7Look For A Pattern47 runs 28, 16, then 6: length 3.
Each arrow is one digit-product, so the number of arrows is the chain length.
3.OA.C.7Look For A Pattern246 multiplies all three to 48, then 32, then 6: length 3.
For a three-digit number the first step multiplies all three digits, then the rule continues the same way.
3.OA.C.7Look For A PatternTesting big digits gives 77 → 49 → 36 → 18 → 8, length 4.
Listing chain lengths for two-digit numbers shows 4 is rare; 77 is the unique number that takes 4 steps, and its final digit is 8.
3.OA.C.7Make A Systematic ListSweeping the two-digit numbers shows a chain of length 4 is rare, and 77 turns out to be the only one.
Every two-digit number has one definite chain length, so the numbers sort into groups by length that never overlap.
Once every other two-digit number has been checked and rejected, the single survivor has to be the answer.
Just multiply the digits and keep going — counting the arrows gives the chain length, and a little hunting shows 77 takes the most steps!