diff --git a/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.reference b/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.reference
index 08fe4251b69..6cdb80167d1 100644
--- a/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.reference
+++ b/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.reference
@@ -1,16 +1,17 @@
 -- { echo }
 SELECT *
 FROM remote('127.{1,2}', view(
-    SELECT *
-    FROM numbers(10)
+    SELECT number%20 number
+    FROM numbers(40)
+    WHERE (number % 2) = (shardNum() - 1)
 ), number)
 GROUP BY number
 ORDER BY number ASC
 LIMIT 1 BY number
 LIMIT 5, 5
 SETTINGS
-    optimize_skip_unused_shards = 1,
-    optimize_distributed_group_by_sharding_key = 1,
+    optimize_skip_unused_shards=1,
+    optimize_distributed_group_by_sharding_key=1,
     distributed_push_down_limit=1;
 5
 6
@@ -19,8 +20,9 @@ SETTINGS
 9
 SELECT *
 FROM remote('127.{1,2}', view(
-    SELECT *
-    FROM numbers(10)
+    SELECT number%20 number
+    FROM numbers(40)
+    WHERE (number % 2) = (shardNum() - 1)
 ), number)
 GROUP BY number
 ORDER BY number ASC
diff --git a/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.sql b/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.sql
index 75c06704ab9..1a446a80603 100644
--- a/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.sql
+++ b/tests/queries/0_stateless/02003_WithMergeableStateAfterAggregationAndLimit_LIMIT_BY_LIMIT_OFFSET.sql
@@ -1,21 +1,31 @@
+-- Here we use a trick with shardNum() to generate unique data on each shard.
+-- Since distributed_group_by_no_merge=2 will use WithMergeableStateAfterAggregationAndLimit,
+-- which assume that the data on shards is unique
+-- (LIMIT BY will be applied only on shards, not on the initiator).
+
+-- To distinguish echoing from the comments above we use SELECT FORMAT Null.
+SELECT '' FORMAT Null;
+
 -- { echo }
 SELECT *
 FROM remote('127.{1,2}', view(
-    SELECT *
-    FROM numbers(10)
+    SELECT number%20 number
+    FROM numbers(40)
+    WHERE (number % 2) = (shardNum() - 1)
 ), number)
 GROUP BY number
 ORDER BY number ASC
 LIMIT 1 BY number
 LIMIT 5, 5
 SETTINGS
-    optimize_skip_unused_shards = 1,
-    optimize_distributed_group_by_sharding_key = 1,
+    optimize_skip_unused_shards=1,
+    optimize_distributed_group_by_sharding_key=1,
     distributed_push_down_limit=1;
 SELECT *
 FROM remote('127.{1,2}', view(
-    SELECT *
-    FROM numbers(10)
+    SELECT number%20 number
+    FROM numbers(40)
+    WHERE (number % 2) = (shardNum() - 1)
 ), number)
 GROUP BY number
 ORDER BY number ASC